Can certain people move the bitcoin to fiat price up and down more than others, sure, but its within a range. Exchanges on their own or together could collude to hit a certain price within the range that could clear out a few traders, especially if there is a big interest in longs or shorts, its hugely profitable for them

But I think there is a limit to what they can do, I think that if bitcoin is manipulated for any extended period of time, you'd see crazy premiums in the P2P market, like for example the kimchi premium, is a signal when btc liquidity is in demand in a certain market

Maybe I'm also biased because people who call manipulation are mostly chartists who are often the biggest cry wolfs because it's an easy catch-all explanation. For example someone can claim market manipulation but in that time, a government tax season could be happening creating selling or miners didn't get refinancing on loans and need to sell and you see big selling, but to find and date these effects from around the world is hard so you just summarise it as whales selling lol its so cringe

Personally, I wouldn't categorise a bitcoin market as manipulated because no ones going to shut it down if it gets too volatile, other assets markets can close, when traders can't stomach it, or the central bank comes in to provide a floor you don't get more manipulated than that