That second factor needs to be separate from the originating authenticating service, not that it has to be on a single device hidden away kept in a safe, or on your wrist, or in your pocket. It could be a single device [a server] running bitwarden and you're viewing it through a browser on your <whatever>.
Not everyone wants to follow every single recommendation from a data security perspective, and it becomes an anti-pattern when laymen start using workarounds to not have to comply with the safety recommendation of the week.
Having it integrated with a password manager is less secure than having it as a separate app in a separate device, but it makes it so much easier for the average person that they're more likely to actually use it.
In a vacuum, yes, you're right. It's not as secure this way. I wouldn't use that for something hyper-sensitive like classified systems. But as a system, "less secure but widely used" beats "more secure but most people avoid using it whenever possible".
It's like with the NIST recommendation against regularly rotating passwords. In an ideal world, it's a great ideal to require new passwords frequently. In this world, it only makes people pick bad passwords and append the date or serial number to it. As a system, it's more secure to require strong passwords and then leave them alone until/unless you suspect they've been compromised.
Higher assurance authenticators need more than TOTP. Usually that means adding a knowledge component (ie pin), challenge/response, a physical token, biometric or all of the above.
There are benefits to this. I've left my phone at work, and would have been SOL, except I have a tablet that never leaves my home which can also provide my second factor.
Isn't it in the name "TWO FACTOR"? It's supposed to be a separate device and ability to "across devices" comes as an anti-feature for me.
1) If you're not using password manager, then you're probably using same password everywhere, including your 2FA app.
2) If you're storing your 2FA codes in your password manager, then it's not really a 2nd factor. It helps against password leaks from services, not from a password manager leak.
Ability to synchronize encrypted backup is a different story.