Yep, the big tickets can rinse your budget. I’d choose one you really care about—Topkapı would be my pick for Ottoman history—and stop paying just because something’s on every itinerary.
Hagia Sophia’s upstairs visitor gallery is €25. Worth considering if Byzantine history and mosaics are your thing; otherwise, enjoy the building from the square and keep the money. The downstairs prayer area isn’t a free sightseeing entrance, so don’t count on that as a workaround.
I’d skip climbing Galata Tower on a tight budget. Go to Süleymaniye’s courtyard overlooking the Golden Horn instead: different angle, cracking view, no tower ticket. The mosque and Blue Mosque are free to visit outside prayer times. Paid tea gardens nearby are optional—you don’t need to buy a drink for the courtyard view.
The Cistern would be another optional splurge for me. You can spend plenty of time exploring the bazaars and old streets without buying another ticket. Save some money for eating 😅