Bitwarden

Randomly, some websites seem to have a lot of fun breaking password managers. One inconvenience is sites now often asking for user name and password separately.

Another inconvenience is sites that use six-digit emailed codes instead of passwords. Which is just massively inconvenient because not only do I need to have an email program at the computer I am at, I also need to switch back and forth and copy-paste stuff.

Is there any password manager that works with those? Is there a way to get these codes working with Bitwarden even?