I would like to know why the Gorn was there too, but the Gorn didn’t notice Spock boarding and so there’s no reason to believe Enterprise would have notice a Gorn boarding. It’s also possible it was beamed over when the Cayuga was destroyed to find something or to access the ships systems.
Cayuga is a connie according to memory alpha - confirmed in some background graphics: https://twitter.com/timothypeel1/status/1690018124492349440/photo/1