It's not only meta but also the CMS wiki that holds the contents for wikipedia.de. See this github issue: https://github.com/wmde/fundraising/issues/1086

If you want to have wiki pages edited by your actual users you could also have a script run locally that edits relevant pages using API's action=edit. Script would have your credentials somewhere and do edits as yourself.
This is basically the same thing as with the link to form you enter your username and password but more automatic (for my taste): don't have to enter passwords (two different username/password pairs, actually) every time, you can run it from command line without even touching a mouse or a browser etc.

Or if you wanted to have it fully automatic you could add some mapping from github usernames to wiki usernames. Once github merges the commit the webhook would be fired. Triggered script would map the username of the guy who merged the PR to wiki username, read wiki credentials from the secret file, and do API as this user. But this will be leaking your passwords kind of, unless done some super magic way. So unfortunately some manual step will be needed.

Or you can always push straight into master without doing github pull requests, and have local git post-push hook that would run wiki-editting script as a right user (will be run on the machine of the person who pushed). Just kidding with this "suggestion", of course.