No connectivity (Temporary failure in name resolution)

Hey,

I did a fresh install of Raspian OS v11 (Bullseye) with Pi-Hole on a Raspberry Pi 3b+
I then installed Tailscale via the command: “curl -fsSL https://tailscale.com/install.sh | sh”
I authorized the Raspberry in my Tailscale dashboard and configured with a subnet and an exit node.
I can properly access the Raspberry from my other devices (VNC, SSH) and all seems to be OK.
However, as soon as Tailscale is up on the Raspberry, I no longer get Internet connectivity on the Pi itself (so apps cannot update for instance).

“ping www.google.com
results in: “Temporary failure in name resolution”

When I shut Tailscale DOWN and type: “nano /etc/resolv.conf”
the file content is: “nameserver 8.8.8.8”
and I get proper connectivity

When I boot Tailscale UP and type: “nano /etc/resolv.conf”
the file content is: “nameserver 192.168.1.1”
and I no longer get any connectivity

192.168.1.1 is my main router’s IP in a different physical location and I set it as the ‘Global Name Server’ (with Override local DNS “ENABLED”) in my Tailscale dashboard’s DNS setting.

All my other Tailscale devices are using this configuration just fine.

However my Raspberry Pi just times out.

Would anyone have any hints for troubleshooting?

Many thanks in advance