WAIT!!! there is a way. The trick (at least for me) is to make sure that in the project settings the project folder is set to the parent folder of the project file. Then the entry “project folder” appears in the “places” menu. Weirdly enough it takes you to the .cachedfiles folder which at this point is next to the project file, and not to the parent folder of the project but hey, massive QOL improvement nonetheless.
At any rate, apparently right-clicking on “places” allows to add global entries, which I find rather handy. So yeah, the situation is very livable.
As for the transcoded files, if anything is done in that regard I think it would make sense to have the “special location” defined relative to the project folder/file, so that each project will maintain its own bundle of transcoded files, which helps with archival.