Drop "public" UDP feature?

This is a question that came up while working on a supporting refactor for https://github.com/Open-EO/openeo-aggregator/issues/125. I was slowed down quite a bit with this non-standard "public" UDP feature:

• user johndoe saves a UDP with public=True
• other users can list this UDP under GET /processes/u:johndoe
• other users can load this UDP with namespace u:johndoe

also described in python client docs at https://open-eo.github.io/openeo-python-client/cookbook/udp_sharing.html

I think we nowadays settled on UDP sharing through URLs (e.g. with the official remote process definition extension) instead of this non-standard "public" flag.

Is it still useful/necessary to keep this non-standard "public" UDP feature alive?
Or can we clean that up to simplify the related code paths?

Start by reviewing the UDP sharing behavior described in the issue, the related aggregator issue #125, and the Python client cookbook page on UDP sharing. Compare the non-standard public flag with the remote process definition extension; done requires a maintainer decision on whether to retain or remove the feature and a defined scope for any cleanup.