The bitcoin ledger is a bit of a special case. Coins in a transaction are sent to output addresses identified by a signature which is usually a combination of SHA-256 and RIPEMD-160 hashes of a public key signature. Using coins as an input to a transaction (spending them) requires exposing the public ECDSA key used to originally create the signature.

If a particular address has never sent coins then an attacker has to perform a pre-image attack against SHA-256 and RIPEMD-160 which even for quantum computers would be 2^128 operations (generally believed to be intractable) and wouldn't even require breaking ECDSA.

Since most original coins have never been sent anywhere there isn't a way to directly attack their ECDSA keypairs.

There are, however, plenty of addresses holding (a lot of) coins whose public keys are in the blockchain, making them targets for quantum computing attacks. An attacker could solve the discrete logarithm problem for a key and forge a signature in a transaction sending all the coins owned by the matching signature to a new address owned by the attacker and the transaction would be accepted by everyone.

I think they're saying that we know nobody's using quantum computing to break crypto yet, because nobody's been draining bitcoin wallets.

blockchain ledgers are open and public and you could think of the contents of any wallet as a bounty for cracking that wallet's private key. some of the wallets involved in early bitcoin transactions would make perfect targets - they havent moved in years and are presumed lost. the btc in them is worth billions.