Duplicate FileVault setup using using fdesetup
The first thing I'd like to point out is that institutional has everything to do with your school, company, or other organization which manages your computer.

If that doesn't apply to you (and you'd know if it did) then rest assured that hasinstitutionalrecoverykey doesn't apply to you.

I suspect that your drive is encrypted &amp; backed with your AppleID. To confirm, run sudo fdesetup list -extended and look for an iCloud User listing.