Compact phone for rhythm gaming

So I actually got myself a Sony 10VI at a Black Friday sale and I'm considering reselling it and buying another phone after all.

I used a Pixel 4a before and it's size was perfect for my main use: rhythm gaming (I mostly play D4DJ GroovyMix). I have rather small hands and play with thumbs on wide screen, so I need to stay with compact phones. But the battery was slowly dying on me and I couldn't stand how it heated up quickly.

So what is my problem with the new phone?

It keeps ignoring inputs while playing. At first I thought it's the glass screen protector, but I noticed it gets worse after playing a while and it's usually double taps that get ignored. Swiping also doesn't always recognized. Which is unbearable considering I can't keep a combo and it's taking out all the fun out of my favorite game. At this point I think it's a refresh rate or processor throttling thing? I don't know, but maybe choosing a budget phone wasn't my best idea.

Another thing I dislike is the camera. Technically it's supposed to be an upgrade to my old phone but the pictures all turn out dark and over saturated. I really don't like it... I don't need a super good camera, but I do take a lot of pictures on a daily basis of food, my creative projects, my outfits, my dolls... etc.

A short list what I want from a phone:

• compact size (155mm seems to be my limit)
• good responsive touch screen
• audio jack if possible, I mainly play on the go (I want to try out how bad the delay is with an adapter though...)
• good battery life, should survive a day even with 2h+ gaming and social media
• phone not heating up while 1h gaming sessions (2D game with effects)
• decent camera with ultra wide option
• stock android if possible

I know there is not a lot of options in my size range, I like to check gsmarena occasionally, but apparently I took a wrong choice this time and would like some help. I'm from Germany if that's relevant. Thank you in advance.