That's an interesting point.

I'm also curious how bus stops interact with timed lights. Presumably each time the bus stops, it gets kicked back to the next cycle of green lights (which might be a low-single-digit minute delay).

Hopefully there's a traffic engineer in the audience who can give the real answers.

The way it is done her ein my European city is that the bus stop is move behind the traffic lights. The bus and the system are in radio contact, thus the position is known. The time the bus needs from current location to the traffic lights on green light can be predicted, thus the system can calculate whether to keep the green light till the bus arrives or turn red, let the crossing traffic go and then turn green for the bus again. The less predictable time of passenger getting off and on (takes time when crowded, wheelchair takes time, but can be fast when nobody requires that stop) is behind the traffic lights, thus doesn't have to go into the calculation.

Of course this has limits on density of traffic lights and traffic isn't fully predictable either, but overall this works quite well, giving busses mostly a green wave.