The buttons on wp.org and wp.org/download pages have the right padding (with just 2px of difference on the left and right sides). The difference between designs and production is the label's line-height. In the designs is 16px whereas in front is 1.7. That impacts the button's height.
I played with the value on the inspector, and a value of 1.3 looks good.
Originally posted by @fcoveram in https://github.com/WordPress/five-for-the-future/issues/278#issuecomment-2328186702