Why did a Webshot tab open while recording?

That tab is the recorder. It holds the recording as it is written and closes itself once the recording is saved. Keep it open; closing it early can lose the recording.

The tab is titled with a note that says to keep it open and that it will close once the recording has been saved. It is pinned so it does not get closed by accident.

Why it exists

Browsers suspend extension code that runs in the background. A visible tab is the one place a long recording can run without being paused by the browser, so Webshot puts the recorder there and streams the video into storage from it.

What to do with it

Nothing. Leave it, switch back to the page you are recording, and stop from the control bar or with Ctrl+Shift+X. When the recording is finalised the tab goes away on its own.

If it was closed

Open the popup. If the recording could be kept, Webshot offers to recover it; see My recording was not saved.

On Firefox

The recorder tab is also where Firefox recordings are shown while they run, since Firefox has no background recorder.