From your description of the screen on your surface book, your battery is beginning to swell up and soon the screen will begin to bulge outward and eventually become disconnected at the top of the screen. Your battery needs to be replaced in the screen portion of your surface book. The surface book is one of the hardest laptops to repair. The screen is glued in place with a double sided tape material.
The screen will need to be removed as well as the motherboard before the battery can be replaced. The battery is also glued into place and a scraper will need to be used to remove the bad battery. It is best to have someone who knows how to do this perform the repair. It is extremely easy to break the digitizer (screen) when trying to remove it. A heat gun is required to heat the screen to loosen the glue enough to use a pick to separate the digitizer from the screen back.
Removing the motherboard is also tricky because special torque screw drivers are needed to remove the screws holding the motherboard to the back. The size of the needed screw driver is 3T. There are 3 different sizes of very tiny screws that will need to be replaced in the correct spots. Great care is needed so the 3 micro switches for volume and on/off are not broken.
The speakers can be unscrewed and the latch cables unplugged. The cooling fan will need to be loosened from the sponge retainers. The the motherboard can be moved out of the way enough to get access to the battery. It takes me about 3 hours to change a battery and put everything back into place after cleaning all the old glue.
This happened to the surface book I’m using to write this response. It is working great again and the discolorations and bulge are now gone.