Mac sign in issues

My mac book air from ~2020 has a broken screen but I use an asus brand monitor so my mac is still usable... however I just installed the newest update with an issue... my normal mac has the profile picture that I need to click. In the past I have just dragged my mouse around and clicked on it but this time after 3 hours there has been NOTHING can anyone help by giving a photo of what is on the normal mac screen for the most recent update? Is it the same and I just have bad luck? No idea :(