I remember having problems using tailscale vpn 24/7 and pihole on my home network with the phone pointed at the 192.168 address for DNS. Pages would take 5s to resolve and start loading.
Unfortunately, Pihole was less important than Tailscale and I have to put up with mobile ads.
I'm on iPhone, i found a workaround involving having headscale set the dns using 'magicdns' or something and having that pihole join the tailnet. after that everything is mostly groovy but the individual components don't easily seem to be able to connect to a different vpn.
Unfortunately, Pihole was less important than Tailscale and I have to put up with mobile ads.