If you're making a right-hand turn in the US as a driver and there's a protected bike lane you're crossing through that lane to turn. And, when I sit outside in the summer at one of my usual restaurants with sidewalk seating, there are any number of horrifying combinations of bicycles, ebikes, escooters, and things that look like electric motorcycles routinely blowing through the red light at the adjacent intersection--cause they're in a bike lane I guess.
You cross through the intersection. You don't treat it like an extra lane to pass traffic on the left which some drivers like to do when there is sufficient space or no curb.