Swapping wires in electrical panel to move outlets to different phase of service. Is this safe?
This panel has more problems than you can shake a stick at
Not only do you have the mis-wired MWBC pair in #13/#14/#15/#16 trying to slow-cook a couple of neutral wires, you have a bigger (in terms of time and cost to fix) problem with this panel, namely that 75% of your breakers don't belong there as they're the wrong type for the panel you have. Furthermore, it appears that most of your MWBCs do not have a means for a common maintenance shutoff, which also is a Code violation.
As a result, this isn't just a matter of swapping a couple of wires around and washing your hands -- you'll need to replace 75% of the breakers here just to bring it as close to Code as practical for this panel, given that putting a bigger panel in would make this a far larger job.
Problem #1 -- the double-stuffed panel
Whoever put this panel in was penny-wise and utterly pound-foolish, as they put in a panel that was basically half (or less) the size it should have been.  This forced them to use double-stuff breakers, which provide two breaker mechanisms and handles in a one-space package, connected to the same leg or phase of the incoming service as they share the same contact clip that attaches them to the busbar.
These double-stuff breakers are different from two pole breakers, which have two contact clips on their back and take up two full width spaces, allowing them to attach to both busbars and provide access to both legs of the feeder, and power things that require 240V as a result.  Of course, one can have a breaker that's both a two-pole breaker and a double-stuff breaker.  Those are called quadplex breakers, and one can be seen feeding circuits 9-12 in your panel -- each pole-space contains two breaker mechanisms, with the inner pair and outer pair tied together.
Problem #2 -- multi-wire branch circuit mishaps
It seems that whoever wired this condo wanted to save a few pennies on copper, so they made heavy use of multi-wire branch circuits (MWBCs) to wire it.  In short, because North American light-duty electrical service is delivered as 240V but with the neutral point set halfway between the 240V legs, if you connect two 120V loads in series and connect the neutral wire to the midpoint of those two loads, the only current that returns down the neutral is current that flowed through one load but not the other load, allowing one neutral to be shared between the two hot wires.
However, this requires the hots to be on different legs, and also requires both hots to be shut off simultaneously when you go to turn things off for maintenance work so that you don't get bit by hot B when you're working on something attached to hot A.  Right now, your miswired situation at #13/#14/#15/#16 has neither of those properties, which risks you getting shocked (if you only turned off one of #13 or #14 to work on the garage outlets, for instance), and also is busy trying to light your house on fire, as now you have two hots on the same leg trying to share a single neutral, potentially pumping 40A down a 12AWG wire only rated to handle 20A. (The situation with #4 and #6 only has the former problem, while #9 and #12 are somehow correctly wired to their breaker, but that has other issues which will be detailed below.)
Problem #3 -- the alien invasion
Your panel is a Murray/Siemens loadcenter.  This means that UL, as part of the process to get it listed, tested it with Murray breakers in the panel.  However, only two of the breakers (#3/#4 and #15/#16) in your panel were made by Murray/Siemens to begin with.  The remaining breakers are of the wrong type to be used in a Murray panel (there's a Square D HOMT at #5/#6, and the rest are Eaton/C-H/Westinghouse/Bryant BR breakers) and thus have not been tested for proper compatibility with a Murray panel.
This is what drives the need for breaker replacements here -- the last installer (or installers, even) whacked in whatever they had on the back of their truck instead of getting the correct breaker for your panel.  Note that you are best off shopping at an electrical supply house that stocks Murray/Siemens, or ordering the exact part numbers you need online from a reputable distributor -- the big box stores generally don't have a great selection on these things, which may be part of the reason your panel was invaded by aliens.
Eating this elephant, one bite at a time
Fixing this panel will be a multi-step process, requiring:

Temporary number tags (1-16) to put on the existing wires so that you can tell which wire goes where when rewiring this thing -- if worse comes to worse, you can use flags of masking tape for this and scribble the numbers on with Sharpie
And replacement breakers, namely (these are exact Murray/Siemens part numbers, and are the only parts acceptable here):

a MP21515 (Q21515CT) for #3/#4/#5/#6
a MP220230CT2 (Q220230CT2) for #9/#10/#11/#12
and a MP220220CT2 (Q220220CT2) for #13/#14/#15/#16



The first step, of course, is to turn the main breaker for your condo off.  Once you've verified that nothing's live in your panel, then you can tag the hot wires #1 through #16 based on which circuit in the panel they are hooked up to at this point in time -- we'll be using these numbers later when we hook stuff up to the new breakers.  Once everything's tagged, you can then unhook all the wires from the old breakers, and pull out all the old breakers -- put the ones for circuits #3/#4 and #15/#16 with the new breakers as we'll be transferring those to different circuits as part of this, and dispose of the rest appropriately.
Now that you have all the needed breakers at hand, you can install them into the panel.  The MP2020 goes in the space for circuits #1 &amp; #2, the MP21515 goes into the spaces for circuits #3, #4, #5, &amp; #6, the MP1515 goes in the space for circuits #7 &amp; #8, the MP220230CT2 goes in the spaces for circuits #9, #10, #11, &amp; #12, and the MP220220CT2 goes in the spaces for circuits #13, #14, #15, and #16.
Once that's done, then it's a matter of wiring the new breakers up.  The wires labeled #1, #2, #3, #4, #7, and #8 go back to the same circuits they were always on, while #5 and #6 are swapped to provide a common maintenance shutoff for the #4/#5 MWBC -- this puts the wires labeled #4 and #6 on the inner two poles, while the outer poles get the wires labeled #3 and #5.
Moving on to the right side of the panel, the wires labeled #9 and #12 connect to the two 20A poles of the breaker that services #9/#10/#11/#12, while the wires labeled #10 and #11 connect to the two 30A poles of that same breaker.  Finally, we get to the situation you originally asked about; for this breaker, the wires labeled #13 and #14 connect to circuits #13 and #16 (aka the two outer poles), while the wires labeled #15 and #16 go to circuits #14 and #15 (aka the two inner poles).
Once everything is wired up and tightened down, and the temporary number tags removed to avoid later confusion, then we can button the panel up and turn everything on save for the #13/#16 handle (which will be ganged together), as we'll be moving onto that next -- note that the breakers I got for the MWBCs not only have common maintenance shutoffs, but common trip functionality as well, which will be important when we move onto the garage circuit.
Now that the panel's corrected, there's a much less hinky way to get 240V at the garage
Now that we have the breaker panel straightened out as best as possible (ideally, we'd get GFCI and AFCI protection installed, but that requires wholesale replacement of the panel with a much larger one, something beyond the scope of this project), thanks to the MWBC wiring that's already there, we can make it so you have 240V in the garage without the need to screw around with dodgy adapters.  You'll need three things besides the breakers for this, and those are a Leviton 5844-I combination 5-20T/6-20T receptacle, a wirenut accepting 3 #12 wires, and a piece of red 12AWG wire to add to the existing pigtails.
At the box that you labeled &quot;Outlet on breaker 13&quot;, you'll want to unhook the receptacle from the existing pigtails, and also undo the wirenut that joins the black and red wires together.  Use your new wirenut to add one end of the 12AWG red pigtail to the junction of the black and red wires, and then wire the receptacle as follows (feel free to use the screw-and-clamp backwire system on this receptacle, or the side screws instead if you're more comfortable with those):

Black pigtail to one of the brass screws on the opposite side of the receptacle from the silver screw
Red pigtail to the brass screw on the same side of the receptacle as the silver screw
White pigtail to the silver screw
And bare pigtail to the green ground screw

Last but not least, button up all the receptacles on the garage circuit, and turn the #13/#16 breaker back on.
Now, you have both a standard 120V (NEMA 5-20T) receptacle there, and a 240V (NEMA 6-20T) receptacle that your charger can plug directly into without the need for a dodgy adapter.  This works because the breakers I specified above are common trip breakers, which are required when you are mixing 120V and 240V loads on a multi-wire branch circuit as we're doing here because the common trip function disconnects both legs of the circuit on a breaker trip, thus cutting power to the fault and avoiding a scenario where a one-legged trip doesn't do anything useful because the fault's backfed from the other leg via the 240V load.