Derive contexts from the caller and name timeouts

The go-code skill asks for contexts derived from the caller, with
context.WithoutCancel for work that must finish after a cancel and
context.Background only where no caller context exists. It also names
each operation limit after its operation with the Timeout suffix, in the
file that applies it. Handlers with a background context could not be
stopped by the daemon, and limits named only Time did not say what they
limit.