I enabled it and now it asks me to load a new profile as it does not detect any of the pre-saved profiles.
That's not what is happening. Is not that GSX didn't "detect" the existing profiles, it's just it's not using them, because they completely mismatch the data that is coming from the Navdata, as if they were made for a completely different scenery.
There are some profiles made before GSX was able to use the Navdata API, that used a very questionable method to trick GSX to "work" with Marketplace airports, by using gates name/numbers from the default scenery, and move them to the positions of the add-on airport. This "almost" worked, because the default .BGL was the only thing GSX could read, but if you enable the Navdata, the "real" data will not coming from the scenery, which won't match anything in the custom profile made for the default scenery.
Additionally, while trying to re-customize everything again I noticed that some of the key bindings are not working. I tried to reassign them to my controller as before, and none of them work, except for the F4 and F1 bindings.
You are not supposed to reassign them. To what, considering the MSFS interface doesn't know anything about the GSX editor ? In fact, as the manual suggests, you are supposed to REMOVE the assignment in the sim that conflict with the GSX editors, which are some in the drone camera view.