Hi again!
We never had an exclusive deal with the translation company, so there's no problem for volunteers to go ahead!
I made you manager on weblate - that doesn't come with any responsibilites, only power - your changes no longer need 2+ votes to be accepted. You can contribute whenever you have time, no pressure!
All the strings on weblate are only for the app, the website doesn't have localized strings at all (at the time of this writing).
Strings in the app update shortly after they're saved on weblate - updates show up in https://github.com/itchio/itch/commits - all contributors appear in https://github.com/itchio/itch/graphs/contributors
Hope this answers your questions!