Is Crypto Anonymous? Understanding Privacy on the Blockchain

No. Crypto is pseudonymous, which is a different and much weaker thing. On Bitcoin and Ethereum you are a string of letters and numbers rather than a name - but that string, and everything it has ever done, is published for the world to read and keep. Anonymity would mean nobody can connect the activity to you. Pseudonymity means nobody has connected it yet.
What a blockchain shows about you
More than most newcomers expect. Open any block explorer, paste an address, and you get the full balance, every payment in and out, the exact timestamps and the addresses on the other side. There is no "private" setting and no way to delete an entry. It is less like a bank account and more like a diary pinned to a noticeboard in a town square - unsigned, but complete.
Why the pseudonym does not hold
Because it only takes one link. Buy coins on an exchange that checked your passport, and that exchange knows which address you withdrew to. Paste an address in a forum post, point an ENS name at it, or use it to buy something delivered to your home, and the connection is made in public. Software from firms such as Chainalysis then does the rest, grouping your other addresses around the one that is known. The ledger never forgets, so a slip made years ago still works today.
Are any coins actually private?
Some are built for it. Monero hides amounts, senders and receivers by default; Zcash can shield a transaction's details. They genuinely raise the cost of tracing - which is also why many large exchanges have stopped listing them, making them harder to buy and sell. Privacy and convenience pull in opposite directions here, and there is no option that gives you both.
If privacy matters to you at all, start with the two free habits: let your wallet make a fresh receiving address for every payment, and keep the wallet you post publicly separate from the one that holds your savings. Then read how the tracing firms work and what Chainalysis is.