Is it wrong to store passwords and one-time codes together?

2FA is based on the principle of "something you know" (password) and "something you have" (one-time passwords, Security Key, etc).

If you store the TOTP secrets in the vault, you effectively downgrade the 2FA into 1FA, secured by how well you protect your vault.

If your vault is properly secured with a strong and unique password on top of a second facfor then you should be good. Also keep in mind that if someone manages to breach your operating system, they could technically retrieve the vault content from the memory, or by hijacking your session cookies, etc.

You just have to be aware of the risks involved vs the convenience of having your password 2FA codes stored in the same basket.

It's probably not as safe as opposed to using 2 different machines (one for password and one for OTP)... But I do it still because most of the time I'm just being forced to use OTP when I don't want to.