Hi rose☆,
Thank you for reaching Microsoft Community. I'm sorry to hear about the battery issues that you are having with your Surface Book 2.
Just to make sure I got this right: When the Surface is plugged in to the base (keyboard) charging port while you are working then suddenly you unplug the power supply, it shuts off immediately but you can turn it on again without reconnecting the power supply. Using also the Surface disconnected to it power supply and you run an app using the NVIDAI graphics, battery 2 drains while battery 1 remains at 100%, correct?
Can you please generate a battery report of the device then check if Battery 1 shows up? To do this, follow the steps below:
Open Command Prompt as Admin
Click Yes on the UAC prompt
Type this command below and hit Enter
powercfg /batteryreport
Open File Explorer and access the html file location given in the Command Prompt
Please share us also the battery report generated. I'll sent you a private message where you can reply with the battery report as an attachment.
Additionally, kindly run these steps on your Surface Book 2 then see if the issue persist:
1: Disconnect extra peripherals
Leave the Surface plugged in and confirm that the tip/LED is lit
Disconnect all extra peripherals like USB drives, SD cards and etc.
2: Force Shutdown
Press and hold the Powerbutton for 20 seconds
3: Run Surface Diagnostic Toolkit
See: Fix common Surface problems using the Surface Diagnostic Toolkit (microsoft.com)
4: Check for Windows Update
Go to Windows Settings > Update & Security and select Check for updates
Make sure all updates need are installed including Optional updates
5: Uninstall/Re-install Battery
Check what is the current OS Build of your Windows version by going to Settings > System > About.
Go to Download driver and firmware for Surface, choose Surface Book
Then click the link next to Surface Book 2 then click Download on the next page.
Choose the .msi file that matches your current OS Build and click Next.
Make sure the Surface is plugged in
Open Device Manager, expand Battery
Right-click Microsoft ACPI-Compliant Control Method Battery and choose Uninstall device (install both battery driver)
Note: If prompted with a checkbox stating "Delete the driver software for this device", check the box then hit Uninstall.
After uninstalling, open and run the .msi file you downloaded earlier
Restart your Surface
Hope this helps.
Kind regards,
Marrion