So it looks like it’s connected (per transfer) but it doesn’t appear to be routing. Do you have a DNS entry defined in both the WG settings on the Server & Client? Eg:
[Interface]
Address = 10.0.0.2/24
PrivateKey = [REDACTED]
DNS = 9.9.9.9
MTU = 1320
Check the ‘…’ for WG Client & Profiles, (Cog wheel, IIRC) for the WG Server.
The wg will show all WireGuard related entries by filtering for that entry. You can also do others like firewall, wan, etc.