https://www.youtube.com/watch?v=pLPpl2ISKTg

I don’t know if this will keep the labels, but you can try to sync your contacts via DAVx5 to your nextcloud instance. Use https://f-droid.org/packages/at.bitfire.davdroid on both phones, this app syncs calendars, contacts and notes. In the setup it should be enough to login via URL and credentials. If you run into problems with this setup, let me know, I can try to assist you :)

Once you got that set up, it is a neat way to keep your contacts backed up and synced with other devices like a PC. If you want to dive further into the syncing without relying on Nextcloud, I recommend Baikal.

Good luck!