Why 6 minutes
Six minutes is the length of the six-minute walk test, a standard clinical measure of functional exercise capacity. Outside a clinic it is a good length for a focused tidy-up: long enough to make visible progress in a room, short enough that you will actually start.
It will not drift while you do something else
The countdown is worked out from a fixed end time rather than counted down frame by frame, so putting the tab in the background, locking your phone, or switching apps does not cost you any of the 6 minutes. Browsers throttle background JavaScript to save battery, and that is exactly what makes most browser timers lose time. Press start, go and do the thing you are timing.