Data stored on your device is encrypted using iOS’ own encryption. So your databases are always encrypted and can only be read by DEVONthink To Go after you unlocked your device after a restart.
An additional app-wide passcode that can be different from your device’s passcode secures access to your data. Alternatively you can use Face ID or Touch ID. For usability reasons, individual databases do not have their own password protection, but their password is required to import them from a sync locations.
If these two levels of security do not suffice, e.g., for classified government documents, a specialized data vault, as provided by most government agencies, might be a more appropriate solution.