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I've been able to setup it finally, with Martin's help.

The question for the other remote is due to the runtime, it wants to install it from there. That's because when the runtime reference is created it has set "from anywhere" and Software finds it at the first remote, even it's available also at the same remote the application is installed from. The Software should prefer the same remote, when the runtime is available there. If not, then pick whichever is found first.

I opened an upstream merge request:
https://gitlab.gnome.org/GNOME/gnome-software/-/merge_requests/794

gnome-software-3.36.1-9.el8.x86_64

Since the problem described in this bug report should be
resolved in a recent advisory, it has been closed with a
resolution of ERRATA.

For information on the advisory (Moderate: GNOME security, bug fix, and enhancement update), and where to find the updated
files, follow the link below.

If the solution does not work for you, open a new bug report.

https://access.redhat.com/errata/RHSA-2021:4381

For the record, this change is not needed in the upstream version, at least not in the form it was needed here. Philip found [1] that a more recent flatpak helps in this regard.

[1] https://gitlab.gnome.org/GNOME/gnome-software/-/merge_requests/794#note_1404242