The thing about Wireguard is that it's very simple and minimal. It does just one thing, and that is - establishes a layer 3 tunnel for sending IP packets between local machine and some other peers. It doesn't do mesh, it doesn't do routing (it just knows the IPs of its direct peers and that's all it does), it doesn't do bridging - all this stuff is done by other pieces such as Linux kernel, but not Wireguard itself.

> Wireguard walk-through to bridge two separate LANs

Same or different subnets for those LANs? If they're different and non-intersecting, and if you don't need cross-LAN broadcast or multicast, the simplest option is to establish a Wireguard connection between those LAN's default gateway routers (assuming you can do this), and on each of those routers set up a route that sends opposite LAN's traffic to the opposite gateway (in case of iproute2: `ip route add my.other.lan.subnet/mask via my.other.lan.gw`, how to make this persistent depends on your distro). Then, on each gateway, allow packet forwarding between Wireguard and LAN interfaces (with e.g. iptables or nftables or whatever you use there).

If you can't run Wireguard on gateways, the overall principle holds, but you'll need to distribute routes to your respective LANs via Wireguard-running routers through DHCP or whatever you use for routing on your LANs (e.g. OSPF).

And if your LANs both have the same subnet, or if you need multicast, things get significantly trickier (plus, there's inevitable question of what should happen if two machines on different LANs have the same IP). You'll probably need to run something like L2TP or GRETAP (or something else that can encapsulate you layer 2) over Wireguard.

Or maybe just use OpenVPN in TAP mode (if you want all stuff independent of any third parties) or Tailscale (because it already works).