On two Civi 5.35.1 & Joomla sites, I've got the same issue of bulk emails not being sent, but the CiviMail report stating every email has been sent (0 bounces or replies). The 0 bounces bit of the Mail report is what alerted us to something being wrong. Other Civi emails are working fine. On checking, another Civi 5.35.1 & Joomla site using a different host and DNS provider also worked fine for bulk email.
Eventually by looking at the server's mail delivery logs I realised that the emails had never sent, with an error that looks like
587 I=[126.96.36.199]:48996 X=TLS1.2:AES128-GCM-SHA256:128 CV=yes DN="/CN=*.filteredmx.net": SMTP error from remote mail server after MAIL FROM:<firstname.lastname@example.org> SIZE=3092: 550-Verification failed for <email@example.com>\n550-Called: 188.8.131.52\n550-Sent: RCPT TO:<firstname.lastname@example.org>\n550-Response: 550 No Such User Here"\n550 Invalid sender <email@example.com> DT=2.353s
With help from here - Mosaico mailings not sending - I saw this means bounce processsing had stopped working.
I tried with a different email account from an external domain (ie another email address I have) - and it all worked again. So it seems there's two issues here:
a Civi error notice issue, because Civi appears to be telling the user mails have been sent when they haven't. It took quite a bit of digging (e.g. turning on MailLog in civicrm.settings.php - gave no insight) before I eventually checked the 'Email Deliverability' screen in Cpanel where I found these errors.
and the 'something has changed in the last few weeks' issue - that might have nothing to do with Civi 5.35.x and be more about Cloudflare or Cpanel or our webhosts. What's especially odd is both sites will let me use an external Dreamhost-hosted email for bounce processing, but each of them if I use a correctly setup email account for the same domain the site is hosted at don't work - even tho one is using Gsuite for mail processing and one is using Cpanel.
None of this is urgent any more as we've got CiviMail working again - but still not sure what the wider issue might be (perhaps nothing to do with Civi at all), and thought it useful to track this here because it happened to me on two sites so maybe happens to someone else.