How's this for an idea: seafaring cultures of the Mediterranean can produce ships that are capable of aggroing other ships. Are they they same ships as usual, just with an added feature? Separate ships? We'll cover that later. Important thing is: Mediterranean powers can produce ships capable of Mediterranean ship combat, which will function similarly to land battles. These ships will not survive out in the Atlantic or the North Sea. They can try, but all that money and life will be lost.
For that matter, any power with ports in the Mediterranean will have access to producing a combat-capable Mediterranean fleet, but not affordably so. Traditional maritime Mediterranean cultures will be able to affordably produce them, much like how Norse get cheaper access to ships to make raiding viable. Open this up to the Indian Ocean: a nearly copy-paste system will exist for the East, but with cultures appropriate to those seas.
So, same boats or unique boats? Tbh idk. Same boats would be easiest, but would minimize the effectiveness of troop transportation from the Mediterranean to the North. Maybe simply make ship combat in the Atlantic impossible, and/or require frequently stopping at friendly ports to keep alive? Separate fleets, to make the price bonus for Mediterranean/Indian Ocean cultures more valuable? Dunno. Another issue for another time.