CalyxOS (the OS by the same company that hosts Seedvault) does have the restore step in their setup wizard: https://gitlab.com/calyxos/platform_packages_apps_setupwizard/-/commit/6729d65f1271fd59dc0e40754d7f028d418dbab1
Since the time my first try to build LOS failed due to not enough RAM I got a new PC that should be able to handle it, so I might have a try myself soon-ish
Edit: for the moment, to start the restore process, one can do
adb shell am start -n com.stevesoltys.seedvault/.restore.RestoreActivity
With that I was able to restore my installed apps. And even the homescreen was restored (which app icons and where they are placed).
Edit2: I was able to extend the SetupWizard by doing most of the changes from the calyxos repository in the LOS sources. And then I tried the restore after a factory reset and I was asked if I wanted to restore my backup (on USB stick). And after a short while I got my apps back (only 4 were installed when I created the backup), the homescreen looked like it was before, and the handful of settings I checked were also restored.
The patch is here: https://pastebin.com/UfpX4wLh
BTW, it seems that /e/ is going to incorporate this solution in their OS, see