If you factory reset the headset, your child won't lose their purchased games (they are associated with the account not the device). However, if you were to add your profile to the headset first, then add your child, they would not be able to share their purchased games with you, as AppSharing only works from the primary account downwards, not from a secondary account upwards. So either way, you would have to re-purchase those games for yourself if you wanted to play them.
I really don't recommend linking or signing in with another account such as Facebook etc. It can cause major problems. A lot of users report getting banned on IG or FB (due to over-zealous AI), then automatically also lose access to their Meta account, with no way of disputing it.
I'm not 100% sure if the parent must be the primary account holder on the headset (the instructions on Meta's help website are rather vague in that regard), but that's the way I do it on my 12 yo daughter's Quest 3. I buy all the apps, then use AppSharing to share them with her. The main downside is that you can't share DLCs and in-game content using AppSharing.
If Meta isn't properly recognizing that your profile is an adult account, that's a bit concerning. A lot of people have been having such issues where Meta asks them to upload a birth certificate etc to prove their age, but their account gets banned anyway. It's imperative that you both have accounts correctly set up according to your ages and not to use any false credentials that Meta AI might later discover and use as an excuse to block the accounts.
Child accounts | Quest help (en-gb)
You can contact official Meta customer support (I recommend "chat with customer support" here.
