Kee doesn’t trigger the AutoType feature and I don’t think it’s something we’re likely to want to add in future.
We are likely to add some improved support for TOTPs in future but in the meantime, it is possible to use the placeholders feature (KeePass only, not Kee Vault) - Placeholder handling - but bear in mind if we add more specific TOTP support in future, you might have to reconfigure the entry at that time.