Thanks for the input, and sorry for the delayed response — it's been a busy few months on our side.
We investigated it further and it turned out not to be an ArcGIS Enterprise 11.5 issue after all. The root cause was a load balancer configuration setting. Once the LB configuration was corrected, the problem disappeared and the external URL started working as expected.
The fact that the issue only occurred through the external URL and not through the internal URL was indeed a good indicator that the problem was somewhere in the reverse proxy/load balancing path rather than within ArcGIS Enterprise itself.
Thanks again for your feedback and for pointing us in the right direction.