I think right now- If you study a pc ship with a spyglass it shows if they are engaged in battle by
"The Liberator is currently engaged in battle with another ship"
I think adding what they are fighting against to the information would be great for roleplay.
"The Liberator is currently engaged in battle with Cordorian Ship"
This would take away some of the ambiguity of what the other ships are doing and increase the gravity of doing misdeeds at sea, be it against a city state or fanatic whale protecting druids etc.
Ps. Forgive me if this is already the case, it's not so easy to double check.