A question on clarification:
Your LED brake lights should have 2 separate levels of "on"; a lower level for nighttime illumination (turns on with the headlight switch) and a higher brightness for the actual brake lights. Are your brake lights not working at all when the headlights are turned on, or just the nighttime illumination setting?
If it's just illumination, the license plate lights are tied in to the same circuit. Do your new license plate LEDs work? Do your front corner running lights still function? Check the fuse if the whole system is dark.
Otherwise, step 1 is to remove the license plate LEDs and swap back to your old bulbs, then see if the problem goes away. It could be as simple as a blown fuse or your LEDs installed backwards (they're polarity dependent). What LEDs are you using for the license plate?