I wanted to set it up, but the requirement is to use a free hosted solution. (So transifex and crowdin are a no-go, they would be great to get translations, especially crowdin looks very active in that regard) I tried out zanata.org but it's extremely slow... The other option at the time was pootle (http://pootle.translatehouse.org), which doesn't offer hosting but some folks at gnu had a customized instance set up, but they discontinued the service.
I searched for a translation service for a private project and found weblate.org . They offer hosting (hosted.weblate.org) for open source projects and it looks like a couple of people are using it. You need to contact them if you want to set it up for an open-source project though and I didn't want to invest in it without knowing what the end-result would be...
Since I'm also mainly interested in German translations for my own installation, I opted to just use plain .po files and filed merge requests against the repositories. Postorius has translations (not perfect, but a start for the moderators that use my instance) included by now but my merge request for core is still outstanding https://gitlab.com/mailman/mailman/merge_requests/400/ Since I don't use Hyperkitty, I didn't translate that.
Thanks for the reply, Simon! We were thinking of using plain .po-files too, however, we couldn't find the matching "src" folder in our installation, do you have any more details where it or the .po-files may also be located?
Regards, Alex