The "OP_RETURN messages" you're seeing aren't magic signals from the old keys. They're almost certainly spam/dust txs sent to the same legacy addresses by third parties (often "recovery-service" advertisers) once block explorers or bots flag those 2011 UTXOs as interesting.

Anyone can send a tiny output to an address and include an OP_RETURN with some text. They do not need the private key of the 2011 coins to do this.

Explorers usually show all activity on an address on one page, so those spam txs look like they're "related" or "before the move". They're not; they're just separate transactions touching the address.

These OP_RETURNs don't affect spendability and don't "unlock" anything. They're just on-chain graffiti/ads ("key recovery", contact TG, etc.), a pattern we see whenever old/large UTXOs start moving.

If the keys had been sold OTC, the buyer would ask for a signed message or a small peel-test, not random OP_RETURN notes from other wallets.

So the sequence "OP_RETURN notes first, big 10k BTC spends later" is simply bots spamming the address once it hit watchlists. The real spends are the four large outputs in blocks ~9039xx that actually move the 2011 coins; the OP_RETURN txs are unrelated noise.