Controller sync button is unresponsive and console doesn't see wifi networks on Xbox series S

Sync the Controller:
To sync a wireless controller with your Xbox, follow these steps:

Press the Xbox button on the controller to turn it on.
Press and hold the small sync button on the front of the Xbox Series X console (located near the USB port).
While holding the sync button on the console, press and hold the sync button on the controller (located on the top near the Xbox button).
Release both sync buttons when the controller's Xbox button starts flashing. The controller should now be synced with the console.

My name is Fernando I'm an independent consultant, I'm happy to help.

Try this procedure, hope it helps: Plug the power cord back into your Xbox Series X|S; Turn on the control; Press and hold the sync button on your Xbox Series X|S; Press the sync button on the controller until the time it starts flashing rapidly, then release it.

Hope I helped and see you soon

Have you tried syncing the controller to the console? Hold the sync button on the front of the controller and the sync button on the console (on the left side just before the usb) until the light on the controller syncs.

If that doesn't work then try heading over to Settings>System and update the controller to see if that helps.

My controller started doing that (Series S) and was unresponsive (console never shut off, though) and I replaced the batteries and unplugged everything from the wall for a few seconds and restarted using the controller and I haven't had an issue since
(sorry if that doesn't help)

Your console doesn't blink at all after pressing the sync button ? Might be an issue with the front panel board ...
One note though : controller doesn't connect to console using Bluetooth but through WiFi Direct 5GHz band (proprietary variant).