Data Center Takeover on The Blockchain

Rewritten with AI for clarity.

I don't have a deep understanding of how the Bitcoin blockchain works, but my understanding is that if a single entity, or a group of entities acting together, controlled more than 50% of the network's mining hash rate, they could potentially create an alternate version of the blockchain and have it accepted as the valid chain for as long as they maintained that majority. Is that correct?

If so, could they create fraudulent blocks that appear to show many unrelated wallets sending them large amounts of Bitcoin, even though those transactions were never actually authorized by the owners of those wallets? If they maintained control of the majority hash rate for a period of time, could they use those fraudulently obtained coins to purchase goods or convert them into USD before the honest network regained control and replaced the fraudulent chain with the legitimate one?

More broadly, could a very large data center operator, or several of the world's largest operators working together, realistically accumulate enough Bitcoin mining hash rate to exceed 50% of the network? I know the hash rate of AI focused GPUs is probably a lot lower than ASICs.

If such an attack were technically feasible, what would the approximate cost be in terms of electricity? How much Bitcoin would an attacker need to extract through double-spending or other attacks for the operation to become profitable after accounting for those costs?