Can't send or test bulk mail, but test mail succeeds in System Settings / Outbound email / SMTP
The symptom as you describe it seems to be that any mail sent via CiviMail will fail immediately and will cause the recipient to be marked as bounced. CiviMail knows when the remote mail system rejects an email, so if that remote system doesn't work as configured, this is the expected behaviour (frustrating as it must be).

You need to understand why CiviMail is not able to deliver ANY messages but regular "Send Email" delivery works for you in CiviCRM.

Probably the most accessible option is to try a replacement mail provider. A few of those listed in this CiviCRM wiki page on mail providers offer a free tier, but everything has its price.

The more complex option is to debug what's actually happening when those mails get sent. This will involve understanding the code that communicates with your mail system as configured, and making the response from the SMTP server visible. I believe you want to start in civicrm/packages/Net/SMTP.php, CiviCRM fetches this from PEAR's Net_SMTP with this patch applied.

The latter option gives you more insight into the issues you're experiencing and might help some future CiviCRM sites who hit the same issue on your hosting environment. If you are confident at debugging, or can find someone to work with through CiviCRM community, that's what I'd try to do. If you just want to get the client live again, you should probably try a replacement provider (or two).