A guest promoted to host published its own player position as the room's
anchor the moment its readiness gates passed, but readiness is not
alignment: that player could be mid-correction, drifted, or at a stale
pre-seek spot, and every guest was then pulled to the wrong position.
The controller now reads the room position on the old host's clock before
discarding it and hands it to the new coordinator as a transition anchor.
The promoted host broadcasts that anchor, gates the group start, and aligns
its own player to it through the normal seek path; only once the seek has
rendered (or cannot: live, or a render timeout) does its local position
become the room's. A player replaced mid-handover inherits the anchor, and
a paused room hands over its paused position unchanged.
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