I'd like to help you out, but I dare not. I never figured out the boat fares. I only know that they vary. But this website purports to have 2024 fares, so perhaps you can get your answer here: https://istanbulish.com/istanbul-ferry/.
Except within the Metro, there are usually no free transfers on Istanbul transport, so don't forget to throw in an extra TL 15 for every bus, tram or funicular you might want to take. And if you encounter a website that refers to fares below TL 15, you should ignore it, because it is outdated. Be careful with CityMapper; it was giving me the old fares last fall, which were many months out of date at that point. I don't know whether they've corrected their fares; I did notify them.
In addition, neither CityMapper nor Google ever seemed to recommend use of a funicular as part of a longer trip.