Adobdb is pure PHP and uses the normal PHP database extensions (mysql in your case), so I don't think imposes any further limits per se.
I'd say that having max_allowed_packet to 1 MB is quite low for the type of usage you have with Moodle. I have mine set to 16 MB. You could try setting it to that value and see if it fixes the issue, before starging looking elsewhere.
Using Oracle with database enrolment
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