Steam overlay doesn't work properly / at all for sertain games

**Game information**
"Transformice!", "Celeste"

**Distribution name and version where applicable**
Linux archlinux 6.8.2-arch2-1
KDE Plasma 6, Wayland session

**Flatpak info**
*version:*
1.15.6
*gl-drivers:*
default
host

**Problem description**

So, I recently decided to install Steam as a flatpak, to separate "gaming environment" from the rest of the system, and also get rid of system-wide lib32 packages once and for all. At first I thought that the steam overlay wasn't working at all, because in "Transformice!" - the first game that I tried to play - 'Shift + Tab' wasn't doing anything. After that I tried installing Celeste. This time overlay showed up, but... As you see in the picture, it's completely broken. Reinstalling didn't help.

The most strange part is that all other games I installed afterwards work just fine! (one game crashed because it required DX9, but that's not important). UI looks OK, all the menus open just fine, nothing crashes. Example list of tested games: "Helltaker", "Terraria", "POPGOES Arcade", "Geometry Dash", "Baldi's Basics Plus", "Holocure". I decided to stop here, because there were no issues with none of these games.

I don't even know how to debug this problem, and is this even fixable from the user perspective. Maybe steam requires additional permissions? Maybe I need to install some additional packages? I would really appreciate if someone helps me with this.

*This is how Steam Overlay looks in "Celeste". The windows are actually interact-able, I can open different menus, select and copy text, etc.*

*terminal output:*
[transformice-report.txt](https://github.com/flathub/com.valvesoftware.Steam/files/14817829/transformice-report.txt)
[celeste-report.txt](https://github.com/flathub/com.valvesoftware.Steam/files/14817827/celeste-report.txt)

This is output from steam by running it from terminal: I opened the game, and then closed it. I can already see that in case of "Transformice", the overlay didn't initialize at all. Also there are issues with gameoverlayrenderer.so in both cases.

**Does this issue reproduce with native Steam**
Native Steam works just fine with all tested games