What's your problem with DAVx^5? It's completely and permanently free and fully-featured on f-droid. Only the PlayStore version costs money. The authors don't want to make money, but motivate you to move away from Google infrastructure.

If you only need address/phone number sync, then nextcloud is probably overkill, but I use it, and it works great. Also for calendar sync and file storage.

(You don't need to put the community name in the title, especially not with "@", which signifies usernames. Communities are prefixed by "!".)

I've used Nextcloud and DAVx^5^ for years (back when X^5^ was still called DAVDroid). Works great.

That works for me since I use Nextcloud for other things. If you want to sync just contacts and calendars, I'd go with Radicale as I used that successfully before implementing Nextcloud.

If you really want to avoid CardDAV for some reason, maybe EteSync

You may be able to use ActiveSync protocol to sync contacts to mail server like exchange or mailcow, though I never use it myself.

Doesn't SoGo use Activesync? This wouldn't need an app on your phone.

I tried the same setup as you a few years ago. It worked, but I didn't like SoGo for email so moved to Nextcloud/SnappyMail and DAVx/K9 on my phone. Have been using this fine since.