How do I never see this again?

... Ok.

So, Wayland cannot actually directly allow input events to access the system directly.

It instead passes them off, as a request for access, to xdg-desktop-portal, which prompts the user with an access request.

This should only occur once, user hits 'grant access' and then the system remembers this.

(Note that this is a fairly significant problem on its own if the user does not have a mouse and keyboard, such as on a game deck, in situations where the user has no actual way to give inputs that are not moderated by an app)

But instead, it keeps recurring, the system doesn't remember properly, it'll work for a bit, and then ask again.

The reporting of bugs I've seen like this goes back to around 3 years ago, when people/distros/DEs started to switch and then default to wayland.

What I've also seen is far less bug reports from gnome users than kde users, and in at least my own experience, switching to gnome completely solved the 'constantly re-requesting access' problem.

It doesn't fix the problem of 'how do you grant access the first time if you don't have a mouse and keyboard'.

So... it seems to me that the more technically accurate thing to say would be:

xdg-desktop-portal-gnome has actually properly been updated to handle this, whereas xdg-desktop-portal-kde has not.

Because gnome wayland seems to at least remember the granted access once you figure out how to give it once, kde wayland does not.

Please actually do test hyprland and post it, if you can.

I am frankly baffled that such a common issue has been going on for years now and no one has seemingly 100% fixed it... yet every distro targeted at a steam deck or other handheld, which doesn't have a kb+m unless you also have a dock and a kb+m, seems to have gone with wayland, and are just pretending this doesn't functionally cripple your handheld in desktop mode.

Its somehow worse than stickykeys prompt in windows alt tabbing your game: this will lock up your entire control scheme, and seemingly can't actually be permanently fixed or turned off.

My suspicion is that the initial pop up still happens in gnome, but in kde, when you click the grant access prompt... it doesn't actually permanently give the permission; some amount of time or sets of sequences of events will reset the granted access and then lock you out and re-prompt you.

I have no idea. It's annoying as hell. But thankfully it goes away when I quit steam. Maybe try uninstalling whatever remote app that is?

I don't know if you've just never used this feature, but KDE Connect absolutely has a Remote Input option that pings this prompt. Unlike the prompt in the OP though, it has a "Restore on future sessions" checkbox.

I saw someone else in the comments recommend disabling the trackpad on the PS5 controller, maybe that's the big difference as to why Xbox controllers don't have this problem?

There is no way the PS layout is more comfortable. The left joystick is where it is on every other controller because that is where your thumb goes naturally.

Even on the other side, the face buttons are used much more commonly than the right stick in most cases. So they put the face buttons there because it's where your thumb naturally goes.

Typically it's not enough more uncomfortable to complain about it if I was like playing at a friend's place (not that that happens anymore in these last generations, but it was huuuuuuuge in the early 90s), but still more than enough of a difference to never buy one.

What is the argument that the asymmetrical comfort zones you seem to have for each hand make any sense? The joystick placement may be cockeyed, but where your thumbs are comfortable should not be. I just can't understand the argument by PS layout fanboys. Hence the question.

Before Wayland was a thing, Steam used a X11 extension to send Mouse and Keyboard presses, which means that for a while, if you used Wayland you couldn't emulate KB+M with your controller at all.
A while so long, that someone created a work around. Extest is a "adapter" that simulates the old X11 extension Steam was using and sends the keypresses using its own virtual input device, therefore completely bypassing the pop-ups.
While that wasn't its intended function, and it is technically unnecessary now that Steam has added support for the proper 'Wayland way of doing things', I can confirm it still works just fine. I use Steam input all the time with no annoying pop-ups.

It can be a bit annoying to install however. If you're using Arch, grab it from the AUR. Bazzite ships with it OOTB, I believe.

Are you using Steam Input Settings to map those dpad buttons? If so, try setting that back to default, then use AntiMicroX to map keyboard input to your dpad instead.