Sounds like a hard to find solution for free. Tutanota comes to mind, you should check them out. Looks like they give you one free calendar to share and export (plus encrypted email). I'm on their old pricing tier so I can't see whether it has feature parity for the new free tier calendars.
Otherwise you might want to activate some MacGyver skills and combine three services:
- Simple Calendar Pro (from F-Droid repository) for offline calendar access, exporting and lots of customization
- Any supported online calendar for sharing (e.g. Google, Nextcloud etc.)
- A sync tool like DavX5 for full sync (if you have a server to host this) or ICSx5 for read-only sync
Hope this helps you along the way.