they can see, or notified by reddit if you been previously banned, or banned in other subs. they can also message admins to report you as a "serial problem, and admin can ban you sitewide" some mods have the Admins ear. also getting banned from a subreddit does make you more susceptible to a sitewide ban in general, anedotl, but it most likely flags your account. also any future acc, even the ones that are years old is susceptible to be banned.
also certain things can get banned sitewide, like hatespeech or obvious attempts at misinformaiton, or causing divisive arguments. also mods tend to be super anal around reports from other users, if enough reports you, you will get banned, or if you attempt to report other people you will get banned if the mod doesnt like the way you reported someone else, i had several instances of this occur on different accounts.