When I go into Users -> Manage Signups and resend email to users under the tab Pending, it is sent and delivered, so it seems like WP core is sending it out as normal.
Sorry to say, once again, Everything is pointing to Buddypress.
Tried also to install WP Mail SMTP that was suggested here in the forum somewhere. Same problem. Seems a problem with Buddypress 2.9.2 – when Active no emails are going out …