start the motor on muffs and shift her to forward and tell us if the prop shaft is turning. Same for reverse.
Don’t have muffs, so I put the prop back on and backed it into the water, the prop moves in gear both forward and reverse. This is a good thing!!
Yes, it's good the prop turned because this means your lower unit probably doesn't have any issue. In another way, it is also a bad thing. Why? Well, if your original post is true and accurate, the prop wasn't turning then, but there is no explanation why it's turning now. Problems don't just correct themselves, but they can be intermittent. Taking the prop off and putting it back on doesn't "fix" a prop that doesn't spin. (The shaft and hub are splined, so it wasn't slipping just because it wasn't on there tight enough.)
A spun hub that's not "totally trashed" yet can sometimes grip enough at low torque if allowed to cool down. I will hypothesize that you spun the hub when you were out previously. Now that it has cooled down, the rubber isn't as soft, and it now grips better, but not truly like it must to work correctly. It held when you put it into gear at low RPM in your water test. I suspect that the next time you go out and nail it, the hub will spin before you get on plane. You should try that near the ramp, and have a plan on how you're going to get back to the ramp. A good plan would be to buy a spare prop.