By installing App Manager from F-Droid, searching for the Settings app and, under activities, lunching the Settings Homepage Activity, I was able to access the full Settings app of the Private Space. If anyone is interested to modify some options that are not currently inside the Private tab of the Owner's settings app, this is a simple workaround.
So at this point I've checked the NFC settings, and surprisingly the bank app that I set as the default for NFC payments in the Owner profile was listed here in the Private Space as the default too, even though it doesn't exist here at all. It is worth to mention that it even has the little icon indicating that it is part of the Private Space. I'm not sure if installing the same bank app also in the Private Space would provide a temporary solution to this, but I might give it a try and write here if it works until an official fix.