Hi Aditya,
This seems to be the perfect place for a narrow bike lane on each side. Although there are entrances into and out of parking garages, I believe that with the correct separation and a slightly elevated lane, cars will be forced to reach complete stop, look for the cyclist, and enter the parking slowly. It takes also a narrow entrance to the parking, which would make the car drivers to slow down, or else they would experience a sharper part of the physical separation between the car lane and the bike track.
Moreover, it seems like a sunny place, so I would recommend using the opportunity to plant trees on both sides.
Since nothing will actually be removed, I think opposition might come from more “general” reasons, such as “why should you put money into bike lanes”, “things are fine the way they are” etc. Obviously, the counter argument would be safety, that bike lanes attract customers, and that no one ever questions why we put more cement on a road or why we add road shoulders.