yes, the symbol was used by Turks in the past and by other groups but the Ottoman adoption of it is due to two factors one a legend about Osman the First's dream, and because it was the symbol of Rome and the Ottomans thought of themselves as the continuation of Rome. the Ottomans were forcing Caesar not Constantinople to stop calling themselves Roman for a while before they conquered Istanbul.
Culture is something that is tied down to one group it is something that evolves over time from different cultures coming together and exchanging ideas, for example, Greek culture gets most of its roots from the middle east.
The Crescent-star wasn't an Islamic symbol but there was a legend has it that Osman I put a crescent on the top of a mosque after he had a dream that he believed to be a vision. The Crescent-star is associated with the Islamic world mostly because it was used by the Ottomans.
I'm sorry to tell you this, but that's Wikipedia level bullshit. You can't really trust anything that can have ideological underpinnings on the internet. Anyone can make the reality seem upside down by picking and choosing the data that they present. Byzantine use of the symbol has no relevance if it's not a ubiquitous use. This is a universal symbol that is expected to be seen in different settings and it indeed was used as a symbol of the city of Byzantium in early Roman Empire era in 1st century AD, but its use as symbol waned to the point of non-existence in any coins or banners depicted from late Byzantine era in 10th and 11th centuries AD. It bears no importance to find this symbol in a couple of individual cases from a span of multiple centuries. What is important is if this symbol was in prevalent use as a symbol of Byzantium? and the answer is no it wasn't. The Symbols for Byzantium that every traveler, eyewitness and historical witness attests to are the adorned Cross and the two-headed Eagle. You cannot find even one contemporary historian or traveler claiming that Star and Crescent were symbols of Byzantines and or used in their banners and such. But they may have been used locally here and there and anyone with an ideological mission can point out to these anomalies and make it seem this was an important symbol of the era for Byzantines.
Sumerians, Babylonians, Assyrians everybody has used this symbol. The important thing is that why Ottomans chose to use this symbol and the reason why is not because they borrowed it from Byzantines because Byzantines weren't using it a symbol for themselves either. Couple of examples of its use doesn't negate this fact. Use of those marginal instances by Internet historians is not proof. Proof would be if the symbol was known as Constantinople's symbol and then Ottomans start using it all over after they conquer the city. Neither of these statements are true. Ottomans don't start using the symbol until 18th century. Any memory of its use by Byzantines would be completely dead by that time even if it was prevalent, but we know it was not prevalent at all.
So let's see who did use the symbol extensively at the time as a smybol of their state on banners, not just on marginal cases here and there in a building or a coin or two. Memluks. Memluks used the symbol as their official military banners, extensively.
Before Ottomans defeated Mamluks in 1516 there was a back and forth about control of the routes to Mecca and a disputation about who has more control over the city. Effectively Mamluks had more control over the Sharifs of Mecca as Ibn Battuta reports that prayers were made for Mamluk Sultans. This is the reason why Ottomans could claim the title of Caliph only after defeating Mamluks and it would be natural to assume they would also adopt their banner as a banner of Caliphate. But this is only speculation and the true origins of the reasons for Ottomans to adopt the symbol are unknown and cannot be credibly traced back to 16th, let alone 15th centuries and adoption from Mamluks and Byzantines as the event happened centuries later. But if there's any claim to be made about the origins, the Byzantine claim is extraordinarily weak and manufactured by Internet historians with an agenda. The Mamluk claim is much stronger than the Byzantine claim, but in the end it is still a weak claim trying to tie 16th century events to late 18th century adoption. But star and crescent as a banner of Mamluks was quite well known and repeatedly mentioned by contemporary sources (as per a paper by Fuat Köprülü), while the same case cannot be made about Byzantines.
. I managed put the phone down.
