Both process-global caches were keyed by the caller's session/task id alone, so under
gateway.multiplex_profiles two profiles using the same id — a shared `browser_exec session=`
name, or two Hermes sessions whose screens report the same DISPLAY — resolved to the FIRST
profile's cloud browser / cua-driver, and a command issued in one bot's chat could act on
another bot's screen.
The key now carries the routed profile's home key whenever a served-profile scope is active
(`get_hermes_home_override()` set), the same shape `tools/approval.py::_baseline_key` and the
camofox/cloud caches already use; outside a scope every key is byte-identical to before. The
computer_use lookup, install and release paths all go through one `_scoped_sid`, so a release
under profile B never stops profile A's driver; approval-bypass state keeps the bare session id.
Fixes#110032 (report by @wolfyy970, from @vandaimer's manual test on #108914).
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