Need help diagnosing a braking problem.

I would take the vacuum off the booster and cap it. Leave the booster port open to the atmosphere.

If you experience the same issue it is most likely NOT the booster. But if the problem goes away then the booster has a valving issue.

It is interesting that you can pull the brake pedal with your foot and it releases.

But the fact that it self applies suggests the booster is the issue.