I am currently hosting a Feature Service on our Enterprise.
The service was made public and is accessible on ArcGIS Pro. However on attempting to access it on QGIS via the Rest service link it throws a Error: 499. And in one instance it threw the following image.
If we save the token into QGIS it then works. This is intended to be publicly accessible.
Can you share the REST URL for the service? If you can't see it in Q, that would suggest that there's some other issue at play.
You could also follow this guide to use OAUTH to retrieve and store tokens for accessing things from Q.