Thank you for the quick response!
I have switched the MTA back to the SMTP server (messages still not being sent).
I have switched the Sending Email via SMTP setting back to not use Separate Authentication (messages still not being sent)
I know that the credentials are correct for the email login information (because emails are being fetched properly) - but I have updated that as well (messages are still not being sent).
I have turned off header spoofing as well (messages are still not being sent).
Either osTicket is not sending these messages (for some strange reason) - OR they are being blocked BEFORE they even reach my SMTP server (because I am not seeing them as SMTP traffic in the logs). My question is - does osTicket send some messages via PHP and some via SMTP (for example, are the admin notifications sent via PHP at the time of ticket generation and then auto replies sent via SMTP)? I need to diagnose why only the admin alerts are going out and nothing else.
I have also worked with our institutional email admin - the messages are not being blocked by our incoming mail server.
Running out of ideas unfortunately ;(