I use Bazzite in the living room, connected to the TV for gaming primarily.

KDE Connect still operates but can't be used for mouse (and possibly keyboard?) input any more. Something to do with the fedora base no longer supporting what it needs from what I've read

Is there an alternative? It was very very handy for the few occasions I need keyboard and mouse

VNC could work?

sunshine and moonlight

When I was still using Windows I used unified remote and it was great. When I switched to bazzite, I couldn't find a solution that was nearly as good for controlling media and as a mouse and keyboard, including KDE Connect.
So I vibe coded my own app to exactly my preferences and it's been great. I've been meaning to open source it for people that don't mind simple vide coded solutions.

What does this mean? Are these programs?

I used to use unified remote also on windows. It says it supports Linux too - did you try it and it didn't work?

Oh, I'm not actually sure I ever tried to get it working on Bazzite. I feel like I tried or looked into it.
But even if I could, at this point I wouldn't. Having this much control and flexibility over the remote is irreplaceable. I can shape the UX exactly how I want it, without fighting a clunky editor.
There have been plenty of bugs along the way, but it works great now. Still, I have a long list of improvements lined up.
Here are screenshots of the two sections as they look today, it still needs work. The big feature for me is the "Launch Spotify" button. It fades down the volume of whatever video I'm watching, fades up Spotify, and launches it for me. The button then becomes "Switch to Video," which reverses the transition and pulls up Jellyfin or YouTube in Firefox. After that it flips back to "Switch to Spotify," and so on.
The point is for when I don't want to miss anything in a video, show, or movie while I'm doing something on my laptop or phone, but still want music in the background.

yeah sunshine (in bazzite portal) is the streaming server you run in bazzite and moonshine is the client app.

https://docs.bazzite.gg/Advanced/sunshine/

Thanks, I haven't found anything called moonshine for android... I found this:
https://f-droid.org/packages/com.limelight

But that doesn't look like a replacement for Kde Connect to me, unless it includes keyboard/mouse control back to Bazzite?

Sorry if I'm being dense! I am trying to find a new way to use my phone to move the cursor and input text on to my desktop bazzite installation.

moonlight used to be called limelight, that is the same app

https://play.google.com/store/apps/details?id=com.limelight&hl=en-US&pli=1

it includes keyboard and mouse control (touchscreen controls section): https://github.com/moonlight-stream/moonlight-docs/wiki/Setup-Guide#keyboardmousegamepad-input-options