Turkey is a NATO member but under CAATSA sanctions and non aligned in cold war 2. GCC are non aligned in cold war 2.
Just because your big doesn't mean your useful. This is the cognitive bias that led to Obama era USA strategists miscalculations that an India, Kabul, and Iran nexus would check Pakistan and the Taliban in Afghanistan. In the end they could not leading to huge embarrassment for the USA and 20 years of wasted resources. India is not relevant to USA national security nor was it strong enough to dominate S. Asia on the USA's behave. Its strategic importance is vastly overstated by most American foreign policy experts.
Turkey is a NATO member. Is there any part of being a NATO member you do not understand ?
The fight with China is political, military and economic. India is a huge economic market in Asia. USA has won World War 1, World War 2 and Cold War against USSR. USA has alliances of consequence all over the world.
Just like Indian quarrels with Pakistan did not impact US policy during the Cold War with USSR. Pakistani quarrels with India will not impact US policy against China. Pakistani generals understand this and the consequences for Pakistan. Hence the hoopla on geo-economics, not being a part of any bloc, hype on ties with Russia etc.
The worst part for Pakistani generals is that no one in USA or India or China knows how the China-USA rivalry will turn out