What is the proper way to transition from a shared lane to a separated bike line across an intersection?

I’ve recently moved to the area I’m enjoying the bike infrastructure a lot! I’m a bit confused however about how to navigate intersections like the one at Yesler Way and 3rd. Heading down Yesler Way, you share the road with cars, and then the separated bike lane comes in from 4th/Dilling Way.

When crossing this intersection onto the bike lane, do I go on the green light for cars? Or do I go up on the sidewalk and wait for the pedestrian crossing? Or even weirder, do I wait in the car lane, but then cross over with the pedestrians?

Thanks in advance! Trying to be a conscientious road-sharer!