The 502 Bad Gateway looks like a consequence of the Mendix Runtime not starting successfully. The most important error in the log is:
Unsupported pre-analysis migration version: 4.4.0
This suggests that the Acceptance database is in an older migration state that the newly deployed Runtime cannot process. Considering that there has been no active deployment to Acceptance for around 1.5 years, I would investigate the database migration state first rather than focusing on the 502 itself.
One additional suggestion: why jump directly to Mendix 11 for this environment?
Since this is a legacy application coming from Mendix 9.24.6 and the Acceptance environment has not been deployed for a long time, I would first try getting the application successfully deployed on a Mendix 10 LTS version.
For example:
9.24.6 → latest suitable 9 LTS → 10 LTS → validate Acceptance → multiple successful deployments → then move to Mendix 11
Mendix 10 can be used as an intermediate validation step here. Once the application and, more importantly, the Acceptance database migration are working correctly on Mendix 10, you can proceed with the Mendix 11 upgrade.
This gives you a much smaller troubleshooting scope. If the application fails on Mendix 10, you know the issue is related to the migration/database state rather than the additional changes introduced by moving all the way to Mendix 11.
I would recommend:
Also, don't use the Production database for testing this migration, since Production is still active.
Based on the stack trace, I would not manually modify the migration metadata in the database. If the same Unsupported pre-analysis migration version: 4.4.0 error occurs even when deploying to the appropriate Mendix 10 version, I would raise a Mendix Support ticket with the complete Runtime logs and database migration information.
The key point is: first establish a clean and successful deployment/migration on Mendix 10, then move to Mendix 11. That should make it much easier to isolate whether the problem is the old Acceptance database state or something introduced during the Mendix 11 upgrade.
Kindly mark this as the accepted answer if it helps.
I would suggest redeploying the last working Mendix 9 branch again. Once this is deployed, do a deployment to Mendix 9 LTS and confirm that this is working. Once confirmed, deploy the Mendix 10 LTS version, and confirm that this is working. Finally, deploy the Mendix 11 version.
You are trying to carry out a large jump between Mendix versions, and I think you just need to carry this out in stages so the application and data is correctly migrated.
I hope this helps. Good luck!