Under gateway.multiplex_profiles os.environ holds the default profile's .env, so `_run_brv`
building the child env from raw os.environ curated a secondary profile's turns into the DEFAULT
profile's ByteRover cloud account (and prefetched the default's memories into the secondary's
context). The local half was already profile-scoped (`_get_brv_cwd`).
The child env now comes from `build_subprocess_env` and, under multiplex, strips the launch
profile's residue and sets BRV_API_KEY only from the served profile's secret scope — a miss means
no cloud key. Single-profile installs pass the process env through unchanged.
Closes#108993 (report and fix direction by @jonpol01).