I have been tempted many times to try to pour new cement over old, your situation is quite common to many of my constructions.

Over and over, I have been advised not to do this, tempting as it might seem.

I believe that is good advice, with bad cement underneath, pouring old over new is asking for trouble in the future, as cement needs a good foot to last.

I would advise cutting the old cement as closely to the wall as possible, prepare a good underlay, and pour new cement in your garage.  This would also give you a chance to put pex under if if you choose to heat the garage someday, so you kill two birds with one stone.

Just as a house is only as good as its foundation, a cement floor is only as good as what is under it.  If the present cement is cracking and heaving, it will continue to crack and heave, breaking up the new cement on top.