Obviously Jesus didn’t believe Peter was satan...
There are places where it is clear the word is meant to describe a true person with a personality, but if you do a search on the word “satan” and also “devil” in the bible (hebrew lexicon gives similar meaning) you come away realizing that often the word simply means someone is being adversarial. And being adversarial to God’s word and actions is doing Satan’s bidding. Hence the meaning overlap.
I wouldn’t be so quick with that. The Greek word used when Jesus spoke to Peter was used 36 times in the New Testament and in every instance it meant Satan. There is another word for adversary which is not used for Satan but is used in Matthew 5:25, Luke 12:58, Luke 18:3, and 1 Peter 5:8. If Jesus had meant adversary He would have used that word instead.