Have tried several methods posted to show data from ACF repeater sub fields, but so far none have displayed anything for an empty area within ""s.
Shouldn’t this be search through the field and outputting the sub field data?
Your code is not calling get_sub_field() from within a repeater field or flexible content loop, so it has no context that tells it what field it is getting a sub field of. The loop you have is a loop of posts in the active_project post type, not a repeater field or flexible content loop.
I can’t really parse the code you’ve posted, I think there are some errors in it.
get_field('name-of-repeater-field') will return an associative array when you call it on a repeater field; You can just iterate over that array the way you’d iterative over any other array. AFAIK get_sub_field() is only useful if you’re using ACF’s have_rows() loop (as mentioned in the documentation), which you don’t seem to be doing. Personally I never use get_sub_field().