In the background
IPNExtensionTailscale
◐ Close the app instead
A private network between your devices.
What it is
Keeps a secure connection to your other devices on Tailscale.
If you close it
Your devices lose their private connection. Disconnect in Tailscale instead.
The verdict
◐ Close the app instead. A part of an app. Closing it alone breaks something, so close its app.
In Activity Monitor
IPNExtension
From Procession’s guide, in the words the app shows.