Word limit for paper after addressing reviewer's comments
I can now provide an answer to my own question (I hope this is alright): I recently submitted a revised article that was about 15% longer than the word limit to a small biomedical journal. The original version of the article kept to the word limit. In the rebuttal letter, I explained that the article had become longer due to the reviewers' question. This article was accepted without further comment from the editor.

So it seems that at least some editors do not see a problems with longer articles, as long as the original submission keeps to the limit. I suspect that the rules may vary greatly between disciplines and journals and that no journal will ever explicitly state "we do not care about length for revised submissions". My PI was very confident that the article would be accepted, so it may be advisable to ask an experienced colleague in the field for their opinion.