MacBook Air is not shutting down properly: causing rapid battery drain

Make sure to disconnect all external devices including the power adapter prior to initiating Shutdown.

Once the laptop is completely powered off, DO NOT:

• Touch any key
• Touch or even brush the Trackpad
• Connect/Disconnect any devices

If you do any of those things, then the laptop may power back on. It is so hard to avoid them.

For any M-series laptop running macOS 15.x Sequoia, it is possible to prevent the M-series laptop from automatically powering on when connecting the charger or opening the lid:

Prevent a Mac laptop from turning on when opening its lid or connecting to power - Apple Support

Unfortunately it is not possible to prevent the same from touching the Keyboard or Trackpad.

Edit: I prefer to press the Caps Lock key prior to sleeping or powering down a computer so when the Caps Lock LED goes dark the laptop should be sleeping or powered off.

A 2020 model MBA could use either an Intel CPU or an M1 CPU. If it is the former an SMC Reset is justified for failures to sleep, wake, shut down, or charge properly.

Reset the SMC of your Mac - Apple Support