My soap drawer doesn’t drain all of the water out. The button also doesn’t work to pop the drawer open
These sound like two separate problems. If the soap is not completely draining but is partially so then the likely problem is that the line to the tub is slightly clogged. See if you can clean it out.
As far as the drawer is concerned, obviously you can open it some way or you would not be able to use the machine. You can replace it, but personally I would just put the detergent into the tub itself and as long as enough water is coming in that will fix both problems at no cost.