It's Arch. You have to install everything yourself. Probably missing 32-64 libs, vulkan drivers.

I'll just spitball because I do not have these problems, although I do have quite some experience with Steam thinkering and troubleshooting. Don't take my answers as actual solutions.

Controller inputs break constantly. If I use big picture mode, the games will be in some quasi state where it both detects my controller and doesn’t.

When you are not using an Xbox or Playstation controller, and Steam is configured for it, Steam will emulate it using a secondary spoofed input device. This might be your problem. Compare your input devices with Steam closed and opened. Look under the controller settings and thinker with Steam Input for generic controller.

The right click menu in the system tray does not work 30% of the time.

It always works for me on Gnome. I guess this might be a desktop environment problem and not a Steam one. What DE are you using?

Worst of all, when I close a game, steam will not detect that it closes.

I've had this kind of problem when making a Flatpak Qt app that launches another program. I had to specifically spawn the process with flatpak-spawn to not run into flatpak issues. You say that you also have this problem on a native install, but maybe you didn't really start the native install or you are mistaken? I've mistakenly troubleshooted what I thought to be a native process but I was trying the flatpak I also had installed.

In game, the shift+tab menu does not work; half the buttons are unresponsive and the game will crash upon closing shift+tab

I think this problem is because of the same reason as the previous problem. It might not be spawning processes correctly so it borks the hook. Or maybe you are using some very strict memory protection.

Not exactly, mine is kinda borked because of the browser, it performs like crap, something to do with Nvidia drivers, I think, I'm not bothered with choppy scrolling but choppy video and super laggy overlay and big picture are annoying as hell.

I had the same problem in manjaro plasma kde as I have in mint cinnamon.

Is steam the only program you've noticed having issues? If not then here's a scary possibility to consider: Hardware Failure
I recently had my power supply destroy my MB and SSD and there were signs that I ignored just before it all went down.
If you still have your arch install usb available then boot from that and pick the memtest86 option in the boot menu to see if your ram has any faults.

I have almost none of those issues. CachyOS on two desktops. One is AMD CPU/Nvidia GPU, the other is Intel CPU/AMD GPU. Both KDE. I only use Steam native so far. 8bitdo Pro 2 controllers /w USB Wi-Fi 2.4Ghz dongles.

Occasionally a game hangs, but only about often as I had it happen on Windows.

The main problem I'm having is broken video playback on Store pages with their updated wide media player. Turns hardware acceleration on/off doesn't fix it.

Try this or the —no-browser flag

https://github.com/Aetopia/NoSteamWebHelper

So far im not having any issues with steam games (1 day old cachyos install on new (for me) pc, native steam). I know that's not really that helpful but I hope that you get it figured out

Yo me too!

I close a game and Steam thinks it’s still open. Or I close Steam window and can’t reopen it and have to send a Kill signal and relaunch. Using the packaged version with CachyOS, which I believe is from Aur.

Issue with Native I guess since if you launch just Steam, it launches Steam (Native)

For reference I’m using KDE

I had all those issues on arch for a while, but recent (this week) update indeed seems to bork something even more. Not sure if it was steam update or arch os update, but currently steam window have 50/50 chance to become laggy af and unresponsive. Basically making it unusable. Closing to tray and opening again can fix it with same 50/50 chance.

Have no clue how to fix it. Check their github, maybe someone already reported a bug.

For the controller issues, run games with Proton 9.x. As far as I know controllers don't work right with Proton 10.x

One thing I have with controllers is, that when I do the old -Syu and there are OS level packages in there, steam won't detect any controller until I do a reboot, even if the OS itself detects it.

Other than that there are some games that have full controller support but still only work with steam input. It's trial and error with every game.

Also in i3 steam doesn't like being tiled and wants to be floated (does not react to mouse inputs otherwise), but in hyprland it doesn't care either way. If you're using i3 or something similar, maybe this is related?