Unable to login as login page Password Box missing on iMac after recent macOS Ventura update.

If you've entered the User name try hitting the Tab key to take you to the password field.

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Have you tried reseting the PRAM / NVRAM ?

Power off and Remove all USB things except the keyboard from your computer. Power it on and immediately press down and hold Option, Command, P, and R until you either hear the chime twice or see the Apple logo twice.

It will look like your computer restarts, this is as it should.

The second time you either hear the chime or see the Apple logo, let go of the keyboard buttons and let the computer boot up.

I hope this helps.

Did you try pressing enter, or clicking on the icon? Does any of these not show you the box to type the password?

You're welcome.