Is Cağaloğlu Hamam an Ottoman bath?
Yes. Cağaloğlu is an eighteenth-century Ottoman bath. Its historic identity and today's treatment menu are separate things; check current services directly with that operator.

Related questions
Has the hamam ritual stayed exactly the same?
No. Buildings, customs and services have changed over time. A modern sauna, oil massage or online booking should not be presented as an unchanged Ottoman practice.
Does an old-looking hamam have to be historic?
No. Marble, domes and Ottoman-style decoration can also be modern. Look for documented construction and restoration dates if the age of the building matters to you.
How can I check whether a hamam's history is accurate?
Look for the building's own documented history, museum records and restoration research. Separate construction dates from later alterations and the current operator's marketing.