Depending on how your connection is negotiated, it may partially not be possible due to the architecture of Wireguard. There is likely some way to hook into capturing handshakes between clients (initial handshake, key rotations). To determine disconnects and reconnects however is a challenge. There are no explicit states in the connection. The closest thing to disconnect monitoring is utilizing a keep alive timeout on the connections. There are some caveats to using a keep alive timer, however. Additionally, not every connection may use a keep alive timeout, making this a full solution infeasible.
Detailed information about Wireguard session handling can be found in section 6 of this PDF.
Persistent keep alive is configured per connection by all peers (server and client typically). As I understand it, Wireguard’s peer-based architecture will let both client and server peers define an optional persistent keep alive timer in order to send heartbeat packets on interval. Otherwise Wireguard on either peer may keep opening and closing connections for inactivity (or get its connections forcefully closed externally) if traffic isn’t being regularly sent. This can occur even though the network interfaces for Wireguard on both communicating peers remain up.
I do agree that running some kind of health-check handshake service over the Wireguard tunnel is an easy enough way to periodically check the state of the connection between peers.