Salvages the client half of PR #99333. A workspace tile pinned to an exact
owner (connection + target profile) was reconciled via a bare
getLatestSessionMessages(storedId) — the foreground profile's backend — so
a bot tile on another profile never saw its new turns (or saw the wrong
session's). reconcileTileTranscripts now derives a ProfileScope from
tile.ownerRoute and keys the per-tile signature by that route; route-less
tiles keep the legacy local read.
The tui_gateway/server.py `_sessions_sig` cross-profile scan from #99333 is
intentionally not taken: the desktop runs one backend per profile, each with
its own watcher, so scanning sibling profiles would misattribute ticks.
Co-authored-by: stods21 <stods21@users.noreply.github.com>
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