Taproot can make all different types of transactions look identical, including simple payments. Assuming enough of the network updates to incorporate Taproot, there will never be much certainty of proximity to CoinJoin or centralized mixer transactions.
Taproot only hide the inputs & part of the unlocking script which isn't used when spending the input, so some difference still exist between transaction. IIRC only Monero blockchain which could make all different types of transactions look identical.
Help me dissect these explanations from Pieter Wuille:
I know it doesn't apply to every case, but I was under the impression that obfuscating transaction type was the primary privacy gain in the Taproot proposal.