You can find your textbook’s discussion of Istanbul in the section entitled “Cultural Patronage of the Islamic Emperors.” The first subsection in that section is entitled “Istanbul.” The text does not explicitly say how Istanbul “captured the grandeur” of Constantinople, so you will have to infer that from what is actually in the text.
The text tells us that the buildings of Istanbul borrowed from the architectural styles of the Byzantine Empire. For example, it tells us that many buildings in Istanbul, such as the Suleymaniye Mosque, were built in a style that merged Muslim and Byzantine influences. The mosque has tall, slender minarets in the Muslim style, but it also has large buildings with domes that echo the influence of the Hagia Sophia church that was built in Byzantine times. Thus, we can infer that Istanbul captured the grandeur of Constantinople by borrowing from its architectural style.
Istanbul was largely important to Islam simply because it was the capital of a long-lasting Muslim empire. Istanbul did not have much religious significance in Islam. It was mainly important as the seat of the Ottoman Empire.