It seems like the quick filters don't work on FK columns. Ideally, they should work on their text,
The export should export both the ID and the value of those FK columns.
It wasn't possible to filter on foreign key values. I'm sorry, the code is just too hard to modify so late in the lifecycle of the product (given we're announcing EOL in parallel).
I've succeeded to make it export the foreign key values separately, for Excel exports.