Synchronised Traffic lights are interesting because even though you have multiple highway=traffic_signals or crossing=traffic signals after each other on a single way these will all be green/red in the same moment. So this means that a way will not be less interesting as a route even though it has lots of crossings and traffic lights. I'm not sure this is needed, or if you should bother mapping them, but I know of places where this matter.

No, they are not green at the same moment, they require a staggered cycle that allows to pass with a particular speed.

DE: "Grüne Welle"

NL: "Groene golf"

this is a draft