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Hi – Ledger Recover doesn’t change your security at all, so your assets still will remain as secure as before. Important to note if you need to interact with your secret (phrase) you always need to consent!
The (firmware) update runs on the Secure Element. Downloading the latest OS update for your Nano X does not mean that your Secret Recovery Phrase can be extracted. Your security is paramount to Ledger and this will not change. This article explains more:
https://support.ledger.com/hc/en-us/articles/11022833583261?docs=true
If you still wanted to inquire further, reach out at http://support.ledger.com