CI caught this: the Chat UI Playwright run failed because the floating panel
opened during an ordinary chat turn and its Expand button covered the
composer's Send button.
The panel opened because Studio's own chat goes through the same tracked
endpoints as the OpenAI-compatible API, so any conversation looked like API
traffic. That is wrong regardless of the click interception: this panel exists
for when Unsloth is being used as an API server, not when someone is using
Unsloth.
Record on each monitor entry whether the caller authenticated with an
sk-unsloth key rather than a UI session, and auto-open only for those. The
discriminator already existed for other routes; this reuses it.
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