[Coda]

No, E=mc^2 is mostly used for nuclear reactions, not chemical ones. You CAN theoretically use it empirically to determine the energy of a chemical bond by breaking that bond and measuring the change in the mass of the system -- I worked the math for this in an assignment in high school but I don't know if it actually gets used this way in practice.

Rather, rocket thrust works based on the principle of conservation of momentum. When you throw something off the back of the rocket, the equal-and-opposite-reaction pushes the rocket forward.

A simple example that you should be able to work given the knowledge you already have:

A drone weighing 250 grams when empty is armed with a pellet gun. Pellets weigh 1 gram each, and the gun can fire them at 200 meters per second. If you load the drone with a single pellet, how fast will it be going due to the recoil after it shoots?

(I haven't actually WORKED the answer.)

To make this more like a rocket, load the drone up with 10 shots and fire one per second. This takes more work -- you haven't studied the math that would make this easier, so you'd have to work out the math one shot at a time -- but you can see that it starts off at 259 grams going one way and 1 gram going the other way for the first shot, but 250 grams going one way and 1 gram going the other way for the last one -- the same impulse results in a different change in velocity.