I know it’s a slight regression for password managers, it annoyed me at first, but I have made my peace with it as I understand the other security benefits. I’d recommend sorting your password manager out, I use 1Password and don’t have any problems. I think it’s something password managers will need to get better at quickly.
Splitting across two documents seems monstrous and probably insecure?
There's no point in blaming the pages -- blame lies with the password manager or browser/OS.
E.g. on iOS, Safari fills in your username just fine even when there's no password field. Whereas on iOS, third-party browsers (e.g. Chrome) won't. According to 1Password, it's a known bug that is up to Apple to support/fix in WebView. (And the fact that it works in Safari but not WebView seems a little anticompetitive...)