Bridges do move some normally, yes. It may depend on the type of bridge though? Certainly suspension bridges do.
Railways work well in the center of bridges. One bridge that violates this principle is the Manhattan Bridge; it was built before we had fancy engineering simulations or much experience with railway suspension bridges at all, and so the lower deck is a pair of railway tracks on either side of a roadway.
This unusual design is very stressful on the bridge and has resulted in expensive rehabilitation programs.
Floating bridges also don't necessarily need to have fixed points to load and unload. With suitable stabilisation and propulsion, they should be able to move to any number of loading and unloading points. We could have a floating bridge per train, vehicle, or any unit or set of users.
it was supposed to open earlier, but the contractor messed up the concrete pour and is fixing it at their own cost. but that doesn't have much to do with the fundamentals of the floating bridge itself.