Is your ship in Galaxian supposed to stop moving when shooting?

I'm playing Galaxian on a Super Impulse Tiny Arcade. I know that this isn't an exact clone of the arcade but rather a reimplmentation but I've also never played the original and don't know how things are supposed to be.

On this version I noticed that firing my ship's weapon causes it to stop moving while the shoot button is held down. Releasing the button will resume movement along the direction indicated by my joystick.

It feels awkward to have my ship stop moving when firing rather than fire while in motion. Is this behavior found in the original arcade cabinet or any other variant?

Is this behavior found in the original arcade cabinet

No.

I have the same Super Impulse Tiny Arcade Galaxian - as you say, the ship movement pauses while you have the fire button pressed down.

However the original arcade machine ROMs in MAME do not have this issue, the ship moves continuously and smoothly regardless of whether you have the fire button pressed down. This is true whether using a keyboard or game controller.

Of course this isn't proof that the genuine 1979 arcade machine worked this way but I believe MAME developers strive above all for this kind of accuracy.

I think this is confirmed by a careful study of Youtube video Midway's 1979 Galaxian Arcade Game with the 25" monitor! by Joe's Classic Video Games.