This seems to be working as expected. wg1 is up because a Wireguard instance is using it. And the peer is showing latest handshake received 3 days ago (so looks like there's no connection between peers).
Wireguard is not a chatty protocol and only sends data when needed: actual data, initial handshakes and rekeys, and optional keepalive messages.
If you're curious you can get more insights from the whitepaper.
Unless the clock on the device is off, according to the output of wg show, since the device has booted, latest handshake: 3 days, 19 hours, 58 minutes, 12 seconds ago is the last time the peers "shook hands". So before the last handshake (plus some Rekey-Timeout), they exchanged transfer: 8.73 MiB received, 5.59 MiB sent of data.
You need to examine your setup to answer that question.
A Wireguard interface is always "up" in the sense that it is ready to encrypt a packet and send it UDP toward the peer. That does not mean the tunnel is working.
If there have been attempts to send a packet, or persistent_keepalive is configued, the latest handshake should be less than 2 minutes ago. There has been no contact for 3 days.
Would the latest handshake update if it is tried but fail?
If not, I think the remote peer is initiating the connection, then some other services used the tunnel when saw it available. And unless the peer have something connecting to this host the tunnel will stay "down" as this host cannot reach the peer.
I will try to ping from the remote peer into this one when i can get a hold of someone on that site to test this idea.