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Depending how far you want to get into this there are several options. I would consider drilling a new hole in the transom choosing a place you would assume to be wet if you had soaked plywood. Like maybe 2" below existing.
If that comes out wet then try another location or start sounding the transom with a mallet to see if your ears can tell what your eyes can't. I seriously doubt that the entire transom is wet.

My engine mounts were also a little depressed when I repowered a few years ago and the dealer would not install the new motor without me reinforcing it. I used a couple layers of woven roving embedded in epoxy and also filled any holes back there with epoxy resin. I overdrilled a few of the holes to fill and every bit of what came out was bone dry. Unfortunately I did not tell the dealer to mount the motor higher, so I will be doing this in the Spring. That will require drilling new lower holes, and I will get a new sample of the inside of my transom. Boat is a 1964, 16'6".

If you find moisture and don't want to rebuild your transom [which would be a huge job] I would consider contacting Progressive Epoxy. The site is so huge it can be intimidating but you can call and the owner answers the phone. Probably his low viscosity epoxy would be good for this as it is very thin, and will set up even when soaking wet. It could be injected into the areas that are wet.