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fix(web): use local timezone for timestamp parsing and improve session liveness logic

Progress log timestamps are written in local time without zone offsets,
so ParseInLocation with time.Local matches the actual semantics instead
of silently interpreting them as UTC.

Frontend session liveness now prefers server-provided session state over
the recency heuristic, centralizes end-time calculation in
getElapsedEndTime(), and guards the elapsed timer against running for
non-live sessions. Also fixes temporal consistency in tail.go by
capturing time.Now() once per event batch, and uses sessionIDFromPath
in watcher test for correctness.