I’m not sure which down arrow you’re referring to.
Do you have “incompatible” enabled?
This questions was answered in the OP, where I said
I have “include incompatible versions” switched to “off”
F-Droid client 1.7.1?
Yes.
Since yesterday I managed to get it to upgrade Linphone to 4.0.1, by following the process of deactivating and reactivating the F-Droid repos, as described here: