Stabilize realtime startup context tests

[aibrahim-oai]

What changed

• The realtime startup-context tests no longer assume the interesting websocket payload is always connection 1 / request 0.
• Instead, they now wait for the first outbound websocket request that actually carries session.instructions, regardless of which websocket connection won the accept-order race on the runner.
• The env-key fallback test stays serialized because it mutates process environment.

Why this fixes the flake

• The old test synchronized on the mirrored session.updated client event and then inspected a fixed websocket slot.
• On CI, the response websocket and the realtime websocket can race each other during startup. When the response websocket wins that race, the fixed slot can contain response.create instead of the startup-context-bearing session.update request the test actually cares about.
• That made the test fail nondeterministically by inspecting the wrong request, or by timing out waiting on a secondary event even though the real outbound request path was correct.
• Waiting directly on the first request whose payload includes session.instructions removes both ordering assumptions and makes the assertion line up with the actual contract under test.
• Separately, serializing the environment-mutating fallback case prevents unrelated tests from seeing partially updated auth state.

Scope

• Test-only change.