Thermostat upgrade delivers heat instead of cooling
Move the orange wire on the troubled thermostat from O to B
What you are seeing here are fairly classic signs of getting your system's reversing valve control backwards.  In order to do their fancy tricks of being able to heat your house as well as cool it, heat pump systems need to be able to make the indoor and outdoor coils &quot;swap places&quot;, and this is done using a special four-way solenoid valve called a reversing valve.
Sadly, there are two different conventions for the way the reversing valve works, and no clear mapping between them and thermostat wire color codes.  Most systems operate where the reversing valve needs to be energized to put the system into cooling mode, which is conventionally marked by the use of an O terminal designation on the thermostat and in system wiring diagrams.  Oftentimes, this corresponds to an orange wire in the thermostat cable, but different cables may have different color codes, and fat cables may be used differently by different installers.
However, Rheem and Ruud units are a bit different; they require their reversing valves to be energized in order to get the system to heat.  This is denoted by the use of a &quot;B&quot; terminal designation on the thermostat and system wiring diagrams; however, the dark blue wire that is intended to be used for this is rarely available in thermostat cables, so its often wired using an orange or brown wire instead.
To add to the confusion, many electronic heat pump thermostats have a single reversing valve output, denoted as O/B and configured for correct operation through the setup menus, instead of having separate O and B outputs available, as in a mechanical heat pump thermostat.  In your case, your experiments with the jumpers and mode settings show that your system is configured with a reversing valve that must be energized to heat.  Since your new thermostat has separate O and B terminals, fixing this is a matter of moving the orange wire over; on your old thermostat, there was a setting that had been changed to do the same thing.