Close, but now you come into contact with the atmosphere not actually being the same density (in weight/volume as well as in particles/volume) throughout, but instead gets thinner as you get away from the earth.

For simplicity, assume space is actually empty, and the atmosphere gets thinner linearly up until x kilometers above sea level it's completely empty. Then the density will also decrease with height, and the helium balloon will eventually find a spot that matches its density, and stop there.

Again there's so much more to it but as a simplified model this works 😅

Rockets mostly need to fight speed (of the earth revolving around the sun), and indeed in our atmosphere speed means friction, but in space rockets still need a lot of propellant to change their trajectory. As always there's a relevant xkcd: https://what-if.xkcd.com/58/