Hi, @maxandersen.
Sorry about the confusion. I thought you were using Safari. With 1Password 7 and the built-in extension for Safari, we have a function within the 1Password 7 desktop app to copy 2FA automatically. But, it won't apply to 1Password in the browser and the current 1Password for Safari that works with 1Password 8.
When you are on a login form within a browser, 1Password in the browser (the extension) will do the major job of autofilling. There is a different scenario regarding the Universal Autofill with 1Password 8 and Safari. Since you mentioned you are using Firefox and Chrome, 1Password in the browser is in play for the autofill.
As I mentioned in the above reply, 1Password in the browser should automatically fill out the 2FA during the login process. However, some websites' structures might prevent the autofill behaviour. If you see the inconsistent behaviour occur on a specific website, can you share it for me to test?