on server you could try

https://radicale.org/v3.html

to sync calendar and contacts on android you can used davx

and simple calendar app is nice https://www.simplemobiletools.com/

Well I use a Baikal server https://sabre.io/baikal/docker-install/ + A Calendar https://github.com/agendav/agendav and as native on PC /Linux Thunderbird with all the caldav add-ons https://www.thunderbird.net/en-US/ I also have the Tasks.org App to complement the tasks on my android devices https://www.tasks.org/ all synchronized with the baikal server.

Interesting mirroring

You should go with a caldav server. Personaly i prefere Baikal. You could get a overview on the awesome selfhosted site.

Android has a calendar store. An App like DAVx5 would sync with your caldav server and stores the data inside the calendar store of Android. Every calendar App would then work with this cause for the app it looks like a local calendar.

For the web i've found 2 projects, agendav and bloben. I'm not happy with both of them and go with thunderbird on the desktop.

I can recommend Callude, https://callude.wip2p.com (cause I created it)

It's a self hosted, p2p calendar. You run a WebIndexP2P backend, and then you can use any hosted version of Callude, could be the link above, IPFS, electron whatever you like. The UI is also response and works great as a PWA.

It's pretty basic at the moment, but works great as a shared calendar alternative to Google and the likes.

Feel free to ask me any questions.