For WebDAV, you can use DAVx⁵ or Round Sync

DAVx⁵ is fire-and-forget (if you have a reliable server). Nextcloud usually requires work to set up and maintain, but there are lots of resources out there to help. Tons of people use and love it.

Have you tried the fork? It lists one of its enhancements as ‘“Battery eater” problem is fixed.’

Yes it is! It’s really an amazing app.

I use Fastmail for my email and calendar. Their server also supports CalDAV task lists, but unfortunately they don’t have any web UI for tasks. In the past, I have self-hosted Nextcloud for tasks, but ultimately dropped it as I had some issues with my server at the time, so it wasn’t reliable, and I found Nextcloud to be too heavy and slow for my needs. I’m now considering self-hosting Vikunja.

Do you use DAVx⁵?

I use many, but DAVx⁵ is essential to keep my contacts and calendar in sync.

A few other favourites:

• Mull: a privacy-hardened version of Firefox
• Tasks.org: fantastic task app, works well in combination with CalDAV task lists synced with DAVx⁵
• Syncthing(-Fork) for sharing notes and files between my phone, tablet and computer.