Xbox Series S 512GB controller will not connect or keeps disconnecting

The checks in more detail

Start with the power. Replace the two AA batteries, or charge a rechargeable pack, since weak batteries cause disconnects and a controller that will not turn on. Try a USB-C cable between the controller and the console; if the controller works wired, the batteries or the wireless link is the cause. To pair a controller with the console, turn the console on, press the pair button on the front of the console, then hold the pair button on the top of the controller,

between the shoulder buttons, for three seconds until the Xbox button flashes quickly, and it will connect. If the controller drops out, reduce interference: keep the controller within a few meters of the console and away from a router, a microwave, a metal cabinet or a USB 3 hub; if the console is in a closed cabinet, move it. Restart the console fully by holding the power button for ten seconds, and update the controller firmware through the Xbox Accessories app on the console.

Reset the controller by pairing it again. For drift, where the stick moves without being touched, clean around the stick with compressed air, check Settings, Devices and connections, Accessories, and the dead zone settings, which can be adjusted in the Xbox Accessories app. If one controller fails and another works, the controller itself is at fault, and Xbox Support can arrange a repair or a replacement within warranty. Note the controller's model and quote the console's serial number.