2. It pops up a username/password screen. The user types in their credentials for realbank.com.
3a. The owners of fakebank.com use your creds to log in to realbank.com and are presented with a TOTP page.
3b. fakebank.com loads another page that asks the user for their TOTP. The user enters it, still thinking they are logging in to realbank.com
4. The owners of fakebank.com use the TOTP to authenticate as the user with realbank.com.
Entire SDKs to automate this are sold on the black market.
You're sure this is the right web site. But Bitwarden won't fill out the code. What could be wrong? Did the idiots who make this web site change the URL?
Now, maybe you're a far above average user and you would calmly determine the exact cause, assuming at every step that the most likely explanation is you're being phished. Hopefully that's more likely now that you've done this exercise. I would love to believe I'm in this category.
But most users will just be frustrated, why wasn't it filled out? Is there a way to get the code from Bitwarden anyway? There is, it's a bit fiddly but you can do it. Lots of users are going to do that. They might even help each other to give their credentials to bad guys, community spirit.
Hopefully some of those users pause because this is unusual and a few of them will realise in that moment that they're being phished. But experiments suggest most won't.
Maybe the Bitwarden extension should warn users when they try to copy/view a TOTP code by searching for a login rather than using a matched entry.
U2F is my preferred method of MFA, but many services don't support it, and there can be practical issues even for the ones that do. For example, some services support U2F in a browser but not in mobile apps.
The point is the TOTP is precisely as bad as SMS for the common case (phishing) and only safer in a rare case (SIM-swap). This comes with large downsides (losing access).
TOTP is, at best, a very marginal improvement over SMS. This is what makes the online push to complain about services that use SMS 2FA and demand a switch to TOTP very strange.