The Bitcoin designers did not pretend it was anonymous – it’s obviously not to anyone who looks at the architecture! - but the people selling Bitcoin have loudly lied about this since the beginning, however. If you search here you’ll find like 14 years of people pointing out that it’s easily traced and getting a bunch of word salad from the sales guys in response.

My recollection is that Satoshi wanted people to rotate public keys after every use exactly to have anonymity.

And some wallets do this automatically. But if you send a transaction and the change from your previous wallet flows directly to your next wallet, you're not accomplishing much.

That's still not anonymity; it's just pseudonymity with more masks.