fix(dav): Ensure share properties are also set on public remote endpoint

[susnux]

Summary

Ensure that public and internal endpoint both provide the necessary data, so we can e.g. on both request nc:note.
As the share note is not something only for users but also for public shares.

Checklist

• Code is properly formatted
• Sign-off message is added to all commits
• Tests (unit, integration, api and/or acceptance) are included
• Screenshots before/after for front-end changes
• Documentation (manuals or wiki) has been updated or is not required
• Backports requested where applicable (ex: critical bugfixes)

[skjnldsv]

This is on the very edge between a fix and a feat... 😅🙈
Approved nonetheless!