You mentioned “from the perspective of the planet” before, and I think perhaps that’s the key, from the planet’s perspective you fall and rise with equal velocities and equal accelerations, but crucially the planet is moving relative to other things and curves your orbit, so whilst you might might have the same falling and rising speeds relative to it, they’re not in the same direction, so you’re velocity has changed, and from an external perspective you’ve gained velocity from it.

Imagine you start stationary relative to the sun, with Jupiter barrelling towards you (not on a collision course!). From Jupiter’s perspective you fall towards it, and so from the suns perspective you gain velocity opposite jupiters orbit, but you’re not directly head on so it twists your course (let’s say 90 degrees to keep things simple) then as you leave Jupiter it indeed decelerates you relative, but crucially you’re in a different direction now, (from jupiters perspective) you’re pointed right towards the sun, so as you pull away Jupiter is decelerating you in the sun direction (aka accelerates you away from the sun). So you were both accelerated in the anti-Jupiter-orbit direction and then again in the anti-sun direction. Added together those give you a vector which is non-zero, so you’ve gained speed from Jupiter.