Of course if you think of a "keylogger" as a program that can only read keystrokes, then copy-pasting on the clipboard is going to be enough. But we know that keyloggers are not really only "logging keys" anymore, and they can even follow mouse movements, take screenshots, etc.
I think KeePass for example uses some kind of obfuscation, but it's nothing really secure. Here's what they wrote on the official website:
Anyway, it's not perfectly secure (and unfortunately cannot be made by theory). None of the currently available keyloggers or clipboard spies can eavesdrop an obfuscated auto-type process, but it is theoretically possible to write a dedicated spy application that specializes on logging obfuscated auto-type.
I don't know when that was written, but I bet in the meantime lots of keyloggers that target this kind of obfuscation have been written, have they?
Then there's KeePassXC, which if I'm not wrong uses a totally different way of sending data to applications, without relying on simulated keystrokes or the clipboard. I don't know the details, but I wonder if that method is actually secure and if in the meantime any keyloggers that target it have been created.
So the question: are any of those auto-type methods of password managers actually effective, or is it like fighting a losing battle?