Thanks @nathank.
What setting am I looking for when you suggest ‘turning off approvals’?
Things seemed to have been working fine with the new user signup process until 3 months ago, looking at the users list, sorted by newness, from which time group memberships stopped being attributed for new signups (it took that long for someone to complain & prompt me to investigate why they were not getting access to the private forum when that was what they had selected on signing up!)
When I click on newly approved user profiles, their custom user field group-name selections are displaying as expected, so that much is working - but the corresponding groups going by those names are no longer being applied to the user.
As far as I know, other than general forum software updates, I haven’t changed anything since setting up the public vs private group system for my forum late last year - so I assume that a subsequent update, perhaps around 3 months ago, is implicated in the issue.