Thanks for the reply! TL;DR Now it works for me, too! But why?
Longer story:
I first tested my paired device once again; calls didn’t work. I then opened /var/lib/bluetooth/[MAC]/info
and noticed that HSP was the last item on the list. I turned off Bluetooth, moved it first on the list, connected again, and lo and behold - calls worked!
Then I did several cache cleanings, order changes and pairings, and couldn’t make it not work again. The placement of the HSP profile in the list varies, and it doesn’t seem to affect the result anymore; it just works. Oh well! It works, and that’s the important bit