Keep one persistent socket per profile with live work instead of closing
the single socket on every profile swap, so background sessions across
profiles keep streaming at once. A gateway registry owns the primary
(window) socket plus lazy secondaries (own backoff/reconnect); all feed
the same session-keyed event handler. Secondaries are pruned to profiles
with a working/needs-input session, the keepalive pings every open
backend, and LRU eviction spares freshly-touched backends so the soft cap
can't abort a running agent. Approval/sudo/secret prompts are parked
per-session (surfaced via the needs-input badge) so a background turn can
block without hijacking the foreground. Single-profile users only ever
have the primary, so their path is unchanged.
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