After some time of debugging and error_log'ing I've found that message goes directly via SMTP, and is being generated with MIME format by PHP part. You can check it adding $request logging in "include/laminas-mail/src/Protocol" (in "_send()" method).
This is because Laminas Mail you use as mail lib uses Laminas Mime for generating messages as the only way do it. Dancing around options in osTicket won't help for anyone. Please see the code here:
https://github.com/laminas/laminas-mime/blob/2.12.x/src/Message.php
(function "generateMessage()" at line 129)
Probably they (Laminas Mail/Mime) did this in the last version, so downgrading a version of this 3rd party library could help. Will try to do this today.
I wonder does osTicket team have any automatic tests? This issue is easily catchable after any libraries update. I guess sending mail feature is a primary feature of osTicket and should be tested each time before publishing a release.