Okay, so looking it up, seem like the Edge 30 supports ‘Ready For’, which is basically Motorola’s DeX Clone, but I’m assuming your device would need to be unlocked for it to work.
So what I would try is plugging in a keyboard. In my testing hitting the space bar is enough to bring up the pin input on the lockscreen, type your pin in, plug in a external display and hope ready for starts up.
Oh god, pattern lock is gonna make this even more complicated 😵💫
From my testing, no you can’t. The pattern lock doesn’t react to the arrow keys or even the tab key at all.
You used to be able to change your pass with Google’s Find My Device, but looking it up now, it seems they removed the option.
So now your only real choices are plugging the external display and hoping Ready For shows a auth screen or even starts mirroing the display directly.
Outside of that, the remaining option will be trying to draw the pattern blind with a mouse 😵💫