It sounds like you're dealing with a couple of frustrating issues. Let's see if we can get them sorted out.
For the Touch ID issue on your Magic Keyboard, it sounds like there may be some power management settings or issues causing the sensor to deactivate when the keyboard is not plugged in. As a first step, you might want to try resetting the SMC (System Management Controller). This is a subsystem in your Mac that controls functions related to power, and resetting it can sometimes resolve these sorts of issues.
As for your Apple Watch not unlocking your Mac, there are several settings that need to be in place for this to work. Firstly, you need to make sure that your Mac and Apple Watch are using the same Apple ID. Next, check that your Apple Watch is passcode protected and that your Mac has 'Allow your Apple Watch to unlock your Mac' enabled in System Preferences > Security & Privacy > General.
Here are step-by-step instructions for resetting the SMC:
1. Shut down your Mac.
2. Unplug the power cord.
3. Wait for 15 seconds.
4. Plug the power cord back in.
5. Wait for 5 seconds, then press the power button to turn on your Mac.
Please remember to check the battery life of both your Magic Keyboard and Apple Watch. If either device is low on power, its functionality might be reduced.
Lastly, if you're still experiencing issues, I'd suggest reaching out to Apple Support for further assistance. To
do so, simply select the "Support" link that is located on the bottom left-hand side of this forum's web page.
Reference:
- Reset the SMC of your Mac - Apple Support
- Unlock your Mac with your Apple Watch - Apple Support