yes this is possible, just make sure you switch to the feature branch from the files page. THere's a "switch to" interface on this page. Once on a head of a feature branch it will be possible to edit any file.
Unfortunately the "switch to" selection did not help. I tried it with other repos as well, and noticed I can edit the branch files as long as the branch name does not contain a forward slash. The branch I'm trying to edit starts with "feature/..." which explains why it does not work.
Do you happen to know of any workarounds for this?