When I try as input the doi with the Automatic tab, it fills in the access date correctly and uses Vorlage:Litartur. It also works for Internetquelle citations.

Are you using the Manual tab and filling out the the fields manually? Then it is not filled out automatically and you have to input each field manually.

I see you have the pubmed website there and that might be why the automatic tab as a whole doesn't work. Unfortunately pubmed has blocked us because we send them too much traffic :(.

Would it be possible that ve does it xlient aide xoming feim my browser?

In T343151#9110408, @ThurnerRupert wrote:

Would it be possible that ve does it xlient aide xoming feim my browser?

Theoretically possible but would require a totally new infrastructure --- for the time being I think it will be more expedient try to get pubmed central links working again, I've created a ticket here: T344801

Using pubmed ids still works, as does using the doi. Pubmed central urls and PMCs don't work.