Read my 22 FF transom rebuild thread in this forum. You'll see a couple of comments I had regarding water dripping from screw holes near the base of the transom where I removed a transducer. I also had a cracked and seperated top cap. I was able to jump up and down on the outboard and had very minimal flex, but some. I put a shop vac up against the dripping screw holes for like 10 minutes then checked the next day and they were dripping again. When I dug out the plywood core (see thread) there were areas of smelly, black, soaked, rotten wood near any screw hole or scupper. The rest of the plywood was solid and new looking but when I pushed a screwdriver into the solid areas water pushed up out of it so it was damp, just not rotten yet. I'm also pretty sure some of the water was weeping into the transom from wet stringers, but I haven't gotten up the courage to drill into my stringers yet to see how wet they are.
Based on your post and my recent experience with my transom, (1978 22 Family Fisherman), I would say that yours has water intrusion around any screw holes or through hulls but might otherwise be solid. The only other unknown is if your stringers are open cell foam and they are saturated, are they open to the transom and sharing some of the moisture there? Some of the former employees here will know the answer to that. I would seriously consider getting the boat inside, getting any screws and brass tubes removed, get it dried out and then re-seal everything with 5200 so you know you are starting fresh with everything sealed. It could be solid but if it continues to get wet it will get heavy, wet and start to rot.