Replaces the Phase 2A pilot ?sid= query param with an HttpOnly,
SameSite=Lax session cookie. Gateway now derives student identity from
the session (via Platform API's /api/session/whoami) instead of trusting
a client-suppliable id, and checks ownership on every proxied HTTP and
WebSocket Lab request, not just the initial navigation.
Fixes a routing bug found during testing: the fallback route was using
'does this session own a running environment' to decide whether an
unprefixed /api/* call belonged to the Lab UI or the dashboard — true in
both places. Replaced with an explicit LAB_OWNED_PATHS allowlist of the
exact unprefixed paths the existing Lab UI actually calls.
e2e-phase2a.js rewritten to use a cookie jar instead of headers/query
params, with explicit impersonation-rejection tests added. 10/10 passing.
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