Why does my screen shut off when I open the computer all the way?

Sounds like you are facing FlexGate! What happening is as you lift & close the lid you stress a cable which was not correctly sized. The stress causes the cable to fail over time. Here’s a deeper dive The Design Flaw Behind MacBook Pro’s “Stage Light” Effect

As the cable breaks down the displays backlight will finally fail getting to a black screen. Plugging in an external display with the lid closed should work via the external.

To fix this you’ll need a new display! I would get to an Apple Store ASAP! As the window on getting this repaired under warranty is getting close to ending. While Apple acknowledged the issue in the 13” the 15” also had problems too!

Here you need to fight for a warranty exception to get it fixed. Be pleasant but firm! if you get NO, ask to speak to the manager and keep working up the food chain! I would go on a Tuesday mid morning as the staff is rested and more responsive.

If you don’t get relief you can replace the display your self it’s just the cost of the display is quite high! $500 USD for a used display and is getting hard to find, a new one is around $750! Which is why getting covered under warranty while a pain is the better answer.

Here’s the 13” extended warranty program 13-inch MacBook Pro Display Backlight Service Program