When a Handoff Instant Booker is configured with a single meeting type at the router level, the meeting type selector should be lockable or hideable so only that meeting type is visible to the end user.

Currently, the dropdown surfaces all meeting types from the assigned rep's profile regardless of what's configured at the router level. This creates unnecessary friction in the booking flow and exposes options that aren't relevant to the handoff context.

Locking or hiding the selector should have no impact on the rep's existing booking links or public profile.