The answer
The mnemonic encodes secret randomness; the principal anticipated quantum problem is vulnerable public-key signatures used by Bitcoin, not simply guessing the phrase.
What to do next
Follow protocol migration plans and do not type your seed into purported quantum-check websites.
Bitcoin.org wallet security resources
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Trezor hardware wallet
A current-generation hardware wallet for managing keys; it does not make Bitcoin or Ethereum quantum-resistant or resolve a future protocol migration.
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