Without going into details of your goal, technically, one can enter into Private space-specific settings using App Manager https://github.com/MuntashirAkon/AppManager in the PS (it doesn't require Internet access or anything).
Run AM, find app Settings, switch to Activities, find Settings Homepage Activity, launch it.
Disclaimer - though PS is not that developed yet, major settings that are supposed to be accessible to the user are already available - like keyboards, passkeys, etc.
Thus, though AM allows you to access some extra, it's not always hidden for no reason.