I have been using Brave Search for over a year and have been very pleased with the results. I have also seen a lot of good things about Kagi, but it does require a subscription.

Here is Eric’s response: https://ericmigi.com/blog/pebble-rebble-and-a-path-forward

I have had positive experiences with both Radicale and Baikal. I am not sure about the Home Assistant integration, but they both use CalDAV, so I would be surprised if there wasn’t a way of connecting them. iOS has native support for CalDAV, but Android needs the davx5 app (free on F-Droid).