My Gen 2 Prius has been acting weird. What are typical symptoms of the battery going bad?

Hey all. I have a 2005 Prius with 12x,xxx miles and its worked great but has been giving me some issues which I cant seem to figure out. Could it be the large battery going bad? Here is a timeline of somewhat relevant events:

-Sep 2020: Catalytic Converter stolen. I got it replaced by didn't replace the o2 sensor. Muffler shop told me to bring it in and they would install it. Car worked perfectly without it and I somewhat wanted the "check engine" to remain so I can fail my next smog and trade in my car for $1500 as its pretty bad cosmetic condition. Check engine sign has been on since

-Also 2020, my main screen stopped working so I cant use heater,ac etc

-Last month: I started feeling a lack of power when I started driving. returned to normal after about 1 minute and also remained normal for the rest of the day. After about 12 hours of not driving (usually the next day) I would feel lack of power for about 1 minute again.

-3 weeks ago. I got the dreaded red triangle, (!) and also lack of power beyond 1 minute of driving. The fan in the back right seat also turned on (battery compartment fan?) . Engine would also remain running at stop lights and with a high rev. I couldn't go faster than 30mph and engine was reving hard, like it was out of gear. I plugged in a cheap obdII reader and got codes P0037, P0138, P0606. When I cleared the codes it started driving perfectly again, no issues at all, for about 5 minutes, then red triangle returns. OBD says P0037. clearing it and lights went away and worked great again, suggesting its a software issues?

-1 week ago: Finally got the o2 sensor and went to get it installed car drove fine for about 5 minutes with no lights, but unfortunately the red triangle returned, along with check engine, and the (!). Since my main screen doesn't work, I cant see anything on that or go into settings. However, my cheap OBDII sensor no longer finds any faults so I can't clear anything. Car drives a little better but sometimes it jumps into a high rev and remains there until I turn the car off. Rev will 3500 going 40 mph on a flat road. Once I turn the car off an on again, then it will drive normal with rev at about 1800. The battery compartment fan is also on. The engine remains running at stop lights and I'm starting to thing it has something to do with the large battery?

Do these symptoms match with a battery going bad? I know i had a few other issues which cloud the situation a bit. When the battery is going bad, will a cheap obd2 sensor show any codes? Will a fancy obd2 reader be able to see whats wrong?

Any direction would be appreciated. Feeling a bit sad over this. Thanks