After taking a second look at your vid, I hear you pressing the Touch ID button.
What is happening then is normal operation of the button and the OS. I can recreate it on my own MBA under Sequoia.
A single press of the TID button takes the Mac to the lock screen. A second press - or simply touching the button - returns me to the desktop or app I was using.
To me, your Touch ID button appears to be working just fine. It is, in fact, a multi-function button; press it to boot the Mac, simply touch it to ID a fingerprint and proceed, or press it to lock the screen.
Am I missing something?