Steam should be loading a separate controller config for every game, or at very least loading a default profile of "every button is literally the same as on an Xbox controller". A weird SteamInput config shouldn't affect across all games, I think.
Does it act up in Desktop mode? How about if Steam is closed, and you play something from Heroic?
It's possible that a hardware fault is sending insane inputs. Bad connections to the controller-sub-boards? The controller microchip just going batty?
It's doing the right thing - most of the harm has been done with the battery being charged up in the first place. If you can pull power from the wall instead of battery, do it. Ordinary usage will chip the battery down to the charge limit in due time.
I have an ASUS laptop which does not do this. When you turn on the battery limit, it stops pulling power from the wall until the battery is down to the right place. Very rude.
It sounds like they have to wait for support to move from the Steam Client Beta to mainline. That happens on Valve Time, so they genuinely do not know.
SteamOS isn't really meant for any system outside the Steam Deck and a handful of similar handhelds. I'm pretty sure it doesn't have any Nvidia drivers, for starters.
Bazzite and Nobara are the general answers to gaming on any random PC hardware.
Finally!
Terminal/Esc looks interesting
Opening something that's a (mostly) static page works. Doing anything that involves talking to a database, such as aggregating your wishlist or searching for a game, is hopeless.
Try searching for any game, any game at all. Steam can't do it.
You can have VRR when connecting to an external DISPLAYPORT (not hdmi) monitor. The internal panel is 60hz (or 90 on the OLED). You can adjust the refresh rate to any fixed value down to 40hz, but this doesn't happen dynamically.
With fixed frame rate you have the fundamental problem that any time the GPU takes even one clock cycle too long to finish a render, you drop to 1/2 framerate. With fixed frame rate you can't miss by just a little bit, every miss is rounded up to the next full frame.
The thing that I would keep an eye out for is if Valve ever does a refresh with a VRR panel. With VRR, you don't need to have "so much excess GPU power that it's impossible to miss a rendering deadline".
Epic hasn't gone out of their way to make life hard for Legendary/Heroic, yet. I guess that is a kind of support.
My biggest regret with Epic is buying Eastward there, and then whoops the DLC sidestory is available on every store but there. I can only read that as meaning "nobody makes money selling games, to the end user, on EGS. The only money you'll make is from selling directly to Tim Epic for a giveaway or an exclusive."
Am I going to put any more money in Epic? No. Am I going to take the freebies? Sure.
The HDMI port on any dock is output only. You would have to get an HDMI capture adapter to go that route, and watching those live with low lag is problematic. Beware of capture adapters that are USB 2.0 (a lot of cheapos will lie about this).
Another way to go would be Steam Link over wired ethernet.
One last way, which involves only one higher-end USB-C cable, would be to directly plug the deck to the tablet. One (or both) would act in a CDC-ether role to network the two together. (How do you simultaneously access the internet/Steam's servers?). This setup is very fussy on the software side. I have been remarkably unsuccessful at connecting the deck to a laptop in this fashion, but Android is more open to doing "dual role" usb stuff.