Nextcloud is my best pick. Of course, it does much more than calendars, so if you’re looking for a calendar service that does only that it may be a bit overblown.

Big pros:

• Native WebDAV integration out-of-the-box - which means that you can easily export your calendars through WebDAV URLs in any supported app

• Support for importing external calendars

• If you also use other Nextcloud products (like mail, contacts or office) the integration betweren them is quite well designed

On Android then I use DAVx5 to synchronize calendars and contacts from Nextcloud with my phone, and Etar as a multi-provider calendar app.

The closest thing I know (but it only works in the browser) is the Firenvim extension

You can find a good Searxng instance or run your own (it can also run on a RPi)