Align timer/stopwatch start to the next whole second

[bakedpanda]

Summary

• Timers and stopwatches used to stamp endAt/startedAt at the exact millisecond you clicked Start, so their seconds digit ticked over out of phase with the clock and with each other — distracting on a broadcast display.
• /slots/:id/start and /slots/:id/resume now defer the actual state change via a short setTimeout (0–999ms) until the next whole wall-clock second, so all widgets change seconds in lockstep.
• A queued start/resume is cancelled if pause, reset, or a type change arrives before it fires, to avoid a race where the slot starts running after the operator already changed their mind.

Test plan

• Ran the server locally, captured the raw SSE stream with wall-clock timestamps around a start call: the HTTP response returned in ~20ms as before, but the mode: "running" broadcast landed within 4ms of the next whole second (remaining: 59999 for a 60s timer, confirming the countdown's zero-point is pinned to the boundary, not the click).
• Verified pause fired during the pending window cancels the queued start (slot stays idle, never transitions to running).
• Manual check in a browser: operator /operator + viewer / tabs, confirm timer/stopwatch seconds now change in sync with the clock and with each other.

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