I haven't watched the video yet, but it's generally not worth the hassle of setting up mutual TLS if you're already using a peer-to-peer VPN like Tailscale, as the VPN software is already doing mutual authentication.
Edit: A peer-to-peer VPN (or mesh VPN) is one where two systems that are connected to the VPN can directly communicate with each other, instead of needing to go through a central server as with something like OpenVPN. With Tailscale or Wireguard, the peers need each other's public keys to communicate.