Should have looked more carefully.
/usr/lib/i386-linux-gnu/wine/wineserver wine32 [i386]
/usr/lib/x86_64-linux-gnu/wine/wineserver wine64 [amd64]
So the actual providers of the wineserver binary are still there, but nothing is placed in /usr/bin to link to them, as it seems. I cannot say how this is supposed to work in 26.04, but I’ll wager the use of the alternatives system to provide /usr/bin/wineserver hasn’t changed. A proper wine installation from the official repos should put a symlink in /etc/alternatives. This is usually done by some post-install script. I cannot rule out a packaging bug, though, since I’m still on 24.04 and a little tight on disk space, so spinning up a VM is not an option, sadly.
I guess, I should have read more carefully; that explains a lot. And it is one more instance for why it is important to not only revert distro sources to default but also to uninstall such packages prior to a release upgrade. In this case it may even be required to actually purge wine, because otherwise it’s in the “residual config” state (dpkg -l shows rc in the 1st column), which may result in the package manager skipping the configuration step and thus the missing link in /etc/alternatives for the official Ubuntu packages.
I’m really not a fan of 3rd party repos and avoid them wherever I possibly can. This is yet another cautionary tale, I guess.