Most of those not wearing face coverings in the UK are exempt for reasons of disability etc.  Of course they have poorer wellbeing/mental health than those who can wear them  That was true before coronavirus, and it's especially true now everyone is judging and harassing them for not wearing one.

This is a completely pointless piece of work; it's very clear that the groups are not going to be comparable, so you've actually got no idea whether wearing a face covering makes you less happy, because you don't know how happy people were before they started wearing them (rather than comparing completely different groups of people).

And even the people who are just choosing not to wear them are likely outside wider society in some way (i.e. not members of the in-group), thus more likely to have poorer wellbeing regardless.

You might also find that lower anxiety people wearing face coverings experience leads them to be complacent, and take risks in other ways because they think their face covering is a magic shield against disease...