githubTokenFromGhCli cached the outcome of `gh auth token` for the whole
process, including "none": a user who ran `gh auth login` after launching
the Desktop stayed anonymous (and rate-limited) until an app restart, since
only a 401 on a real token cleared the cache. Only a token is cached now; a
null answer (gh missing, logged out, hung) is re-asked by the next hourly
check, one bounded spawn per check at most.
Part of #112615
7b085a734b