Both tools can be used from the terminal like most Linux programs, which should also give you better control during troubleshooting and also in the rarer cases of having to set up/run some more temperamental games. There are also graphical programs that handle Wine/Proton in a more friendly way, such as Heroic Launcher, Lutris and, specifically for Proton, Steam itself.
Auster
Unfamiliar with it, but in the regard of instances going down, specially after my previous main instance died with no signs of returning (again), if you find any interesting posts even on instances seemingly stable, I think it is a good idea to back up those pages. Personally, I would propose methods like Internet Archive's Wayback Machine and its alternatives like Archive Today, the print to PDF option from browsers, and/or saving a given page as a MHTML bundle.
Found something: Apparently Recochoku occasionally sells music videos, but the store is blocked outside of Japan.
Yeah, things like interest of the right holders, contractual limitations and availability of a given media do play a part on getting published on a given platform.
Other than GOG's withering "movies" section, I only remember of two that aren't overly niche, DLsite and Fakku (both mainly porn stores). Maybe Itunes' videos are DRM free, but I haven't tested and still it would break the "no app" condition since it's required for payment and download. Also maybe Itchio and Gumroad have something on videos too, since they don't limit the types of media allowed there, but I have yet to confirm.
GOG tried, but either gave up or wasn't able to keep supporting it (their communication is bad so hard to pinpoint). Now their movies section is just collecting dust, like Humble Trove was in the months before the old model was axed.
There are cases where AppImages aren't viable indeed, like with programs that require ring 0 access. But limitations exist for all formats, so perhaps another good alternative is having multiple versions of a given program, like downloading the equivalent deb package through apt while also keeping the appimage version. It would bloat the storage for a potential automated configuration, but it should help with ensuring compatibility.
One thing I like to have with me is the AppImage version of programs when possible, since they usually work out of the box. Also helps ensuring I don't depend on the availability of whatever package manager the system uses.
Blocking everyone and every community you see from Facebook's new parasite social media could be good, me thinks.