The registration emails are being successfully sent; I just tested registering an account and had your board send the registration email to mail-tester.com. You can see the results and detected issues here: https://www.mail-tester.com/test-xwfbl
These results imply that everyone not receiving the emails is likely missing them because your email is being dropped or trapped as spam before ever reaching the recipient's mailbox.
Probably the top thing that affects everything else is that you're sending from a gmail.com email address, through your altervista.org hosting service mail servers. If you need to stick with using this gmail.com email address, you probably need to configure your phpBB mail settings to also authenticate and use the gmail.com SMTP server, too. So that the mail is coming from mail servers that "agree" with the actual email mailbox claiming to send the email.
Alternatively you could create (or acquire service that lets you create) a mailbox on your altervista.org hosting account itself, so that you're sending as "email@example.com
" or similar through the altervista.org hosting service mail servers, instead of as the gmail.com account. This is the approach also recommended in Knowledge Base - EMAIL - Easy setup (NOT SMTP)
Both approaches have their advantages and disadvantages. I prefer using an external service via SMTP, because phpBB's error reporting in cases where sending email fails is better when using SMTP. But its possible your hosting account might block you from using external SMTP services, and so creating a local mailbox may be the easier or only option.