Manuel Quiñones [off-list ref] writes:

that can be fetched from the remote. My proposal: Add the timestamp of
the last fetch to the message. For example:

$ git switch main
Switched to branch 'main'
Your branch is up to date with 'origin/main'. Last check was 2 hours ago.

It looks like the timestamp of file `.git/FETCH_HEAD` would be enough
to implement it.

Not generally.  Your last fetch may not have been about origin/main
(e.g., "git fetch origin next"), or it may even have been about a
totally different remote (e.g., "git fetch elsewhere").

The timestamp of the last entry of the reflog of origin/main may be
a lot better place to look for the information, if available.