Replace 240 receptacle with one or two 120
Yes, you should be able to do this. But along the way, you need to fix the problems.
A NEMA 6-20 is supposed to be hot/hot/ground. It is NOT hot/hot/neutral. But yours is wired up as hot/hot/neutral. In the US, black &amp; red (and blue) are hot, white is neutral. Ground is green or bare or, fortunately for you, armored cable. So the first step is:
Make this a valid 6-20
You don't actually have to do this, but if you actually wanted to use the 6-20, you would want to make it safe. Ground is not neutral.
To do that, cap the neutral (since you aren't using it) and instead connect the ground pin of the 6-20 to the metal box. That doesn't always work, but with armored cable and metal boxes that is the normal way to do things. You can get a green wire with a screw attached and screw it into the metal box.
Switch to MWBC
You can get a single 120V 20A circuit easily - just use one hot + neutral. But you can actually get two circuits. This is an MWBC - Multi-wire Branch Circuit. Each circuit gets a hot (red or black) and they share the neutral (white).
The two circuits have to be on separate poles and common shutoff - but that's already done, so this one is relatively easy. Plus everything gets grounded to the metal box. There are a few ways to proceed. The simplest that I can think of is:

Get a 5-20 dual receptacle. This has 2 20A 120V receptacles, which can accept plugs from any standard 15A or 20A 120V devices (like vacuum cleaners).
Break off the common tab on the hot side. Do NOT break off the common tab on the neutral side. Which side is which? No guarantees, varies by manufacturer/model, so check the instructions.
Connect red and black to the hot side - one to each screw.
Connect white to one of the neutral screws.
Connect ground with a green wire/screw to the metal box.

AFCI and/or GFCI
Depending on specific code requirements, it is likely that this circuit (120V instead of 208V/240V) now requires AFCI and/or GFCI, depending on location. The easiest way to retrofit AFCI and/or GFCI for an MWBC is to replace the double 20A breaker with a double 20A breaker that includes the necessary functions. That is different from a single 120V circuit where it is very easy to use a GFCI/receptacle combination - but those generally don't support MWBC.