What would happen if you jumped out of a moving spacecraft?
If the spacecraft is not accelerating, the astronaut leaves the airlock and just floats outside, not moving relative to it. If the rocket is accelerating they "fall" down towards the stern from the perspective of people onboard; the astronaut would instead say the rocket is accelerating "upwards" and they are just floating.

In space, away from gravitational fields and in vacuum, only relative motion matters. You cannot tell whether the astronaut and spacecraft are moving at a high or low velocity compared to the rest of the universe just by looking at the two of them. So one can flip between the perspective that the craft is fixed and by turning on the engine it makes the astronaut (and everything in the craft) is accelerated, or the the perspective that the astronaut is floating in place and the rocket is speeding away. They are equivalent.

Astronauts leave spacecraft like the ISS all the time, and only experience free-fall despite the station moving at high speed around the Earth. As far as I know nobody has ever done a spacewalk when a craft is accelerating, for obvious safety and sanity reasons.