However, Amazon Prime on the same setup gets me 720p at most. (This is a regression because I _know_ I used to watch the first few seasons of The Expanse in 1080.)
Which add-ons allow you to watch Prime in 1080p on Linux? I wasn't able to find them.
At one point I experimented a bit with making an addon myself, and it's possible to intercept the requests and spoof the UA/platform to get URLs for the HD streams, but then it goes to VMP/widevine and is a bit beyond my abilities. Best I could get was for the HD quality option to appear in the UI, but with a complaint that it wouldn't work because I needed to update or use a different browser.
Now pretty much the only time I use Prime video is for the occasional watchparty, and I'll just pirate the stuff I want to see in HD.
I'm running KDE and have it configured to disable the compositor when an app goes full screen. Maybe that's your issue? Try turning off desktop effects and screwing around with your compositor settings.
Edit: I want to point out that since my GPU can't handle 4k the desktop resolution is limited to ~2k (whatever the highest was that it can handle at 60Hz--I forget now haha).