Calendars and contacts are tricky, it's a lot of work in the background. Google, MS and Apple have really, really integrated those into email and that convenience is what your looking for.

I pulled them out of google and I host them myself, but I don't need to share. and it was a lot of work.

If you want "smooth", you need a service to do this for you, there isn't a way around it.

I use a paper calendar, I don’t trust technology.

I'd like to suggest NextCloud? But if public, and thus, sharing events, maybe Friendica?

I store my calendar in Nextcloud. I sync my calendar to my phone with ICSx⁵. I open my calendar on my phone with Etar.

I use Fossify. Works like a treat but you need a third party online account for CalDAV sharing. And I agree seeing it up was a bit weird.

My family is using TeamUp (https://teamup.com/). But Nextcloud is also a good suggestion.

How are you sharing with others? Read only or do you want others to be able to add/edit events?

If sharing just for yourself, NextCloud or sync a calendar locally with SyncThing.

Or a paper planner, and "syncing" means having it with you.

If selfhosting is an option, you could look into Radicale.

You can read more about the sharing part in the Github Wiki

Hope this helps.