KeePass can also generate TOTP codes. Kind of ruins the point of these codes, but if you're already storing the QR codes on it, you can go a step further and just get KeePass to generate the output code for you.
However, storing 2fa codes alongside your password is still more secure than not. If the service password is compromised without the 2fa seed (main threats: MITM, phishing), the one-time password prevents the account from being immediately compromised.