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> It seems to me that it could have been a misunderstanding, in that the ledger device can’t export the key itself, and you just enter your 24-word seed phrase into the software for it to get split.
no, that would be extremely unsafe: your seed could be captured by keylogger malware on your computer. you should NEVER enter or type your seed words on a computer of phone!!!
The Recover service shards (i,e, splits) your seed in 3 pieces (called shards) and encrypts each piece, and this is done on the device, for safety.
Then the 3 encrypted seed shards are sent to ledger live via USB or bluetooth, and Ledger Live will in turn send them to each of the Recovery service safekeeping companies.
So it is only encrypted shards of your seed that leave the ledger, and this happens only if you sign up for the service and also confirm the action on the device itself.