I setup AdGuard DNS on the network I host my services on and made Tailscale use it as a second DNS. This let’s me access services using domain names. I’m sure you can do something similar with zerotier but I’ve never used it.
Also, it doesn’t have to be AdGuard DNS. Any DNS will be fine.
https://tenekev.com/posts/internal-dns-for-your-tailscale-network/
I don’t think about neovim being separate to vim, sorry.