After entering my Apple ID password to sign out of your Apple ID on my device, howl long does it take to see "Tap erase" on my device

Have you tried entering your passcode as the Related Article above states you should do?

From the article.

From your device's Lock Screen, try entering your passcode until the "[Device] Unavailable" screen appears and your device asks you to try again later. When you're able to, continue trying to enter your passcode until the "Security Lockout" screen appears and you get the Erase [Device] option in the bottom corner of the screen.