I checked the media gallery, and when uploading something there, it didn’t give the php warnings, only a permissions warning.
I had chmod’ed the uploads folder previously but it seems I misread the WordPress page about the exact chmods (https://codex.wordpress.org/Changing_File_Permissions) and implemented the first table 755 (should have been at least 775).
Gosh, such a basic error. Sorry for waisting your time
PS: Keep up the good work, BuddyPress is an amazing piece of software (and even the default look is so sleek!). Thumbs up.