If you use an iOS device you can use a tool like the iPhone Backup Viewer to extract the secret key.
- Open the backup using such a tool
- Find the Steam App:
com.valvesoftware.Steam
inAppDomain
- Extract
Documents/Steamguard-[your Steam ID]
- Open the file using a text editor and look for the text
otpauth:\/\/totp\/Steam:[your Steam login]?secret=[TOTP secret]&issuer=Steam
. - Copy the value of
[TOTP secret]
info the TOTP Seed field of the TOTP Setup Wizard.