If the resistance have a slightly faster top speed than the FO how did they not outrun them? And why would running out of fuel slow them down? It’s not lazy writing it’s incompetent writing but we have your permission to not like it so that’s ok!
I'm going to be boring and science-y for a sec. They were limited to sublight while enacting Leia's plan, as any hyperjumps wouldn't get them away from the FO who could track them. So they've got the pedal to the metal. Now, one of the things we don't see much is how fast "sublight" is in Star Wars. Over in Star Trek, they have operational guidelines. "Half impulse", "quarter impulse", and "full impulse" are more about acceleration than top speed. For normal operations, they limit themselves to .25c because much faster than that and they have to start taking relativistic effects into consideration. In combat and other emergencies, where speed is a lot more important as a tool, they'll go past .5c, but usually not much beyond .75c...
In Star Wars, "going in full throttle", those X-wings looked to be going... maybe a couple hundred miles an hour relative to the surface of the
Death Star. The
Tantive IV, desperately trying to get away from the
Devastator, looked to have been going maybe a thousand miles an hour. Given that we already engage in aerial combat at and beyond the speed of sound, I like to think that the apparently slow speeds of those ships is a conceit like sound in space -- there to help the audience parse what's happening, rather than an accurate depiction of actual events. If the
Tantive IV had whipped past a stationary camera at suborbital speeds, it would have been a whitish smear on the movie screen, gone in two frames.
But the same thing applies in both of those universes, as well as ours. Whatever the normal operational speed practices, if you keep the engines on full, you'll keep accelerating toward c, and your rate of acceleration is a factor of thrust-to-mass. What was at work in TLJ was that the Resistance ships were smaller with big/many engines, and so had better acceleration than the FO ships. So the whole duration of that chase, they were pulling away. But the FO ships were also still accelerating, albeit more slowly. So when a Resistance ship ran out of gas, it was no longer accelerating, just coasting. It would get outpaced by the remaining ships still under thrust, and eventually overtaken by the also-still-accelerating FO ships.
As long as your fuel source holds, you'll continue accelerating indefinitely, but in a decreasing curve as you get closer and closer to the speed of light. It'll take more and more power to keep mounting those decimal points.
What was lacking was any point of reference for how fast those ships were going relative to surrounding space. They might have been zipping along at several million miles per hour, but we'd have no way to tell, so it looks slow, because the camera is mostly keeping pace with them. This is, of course, also not taking into consideration tactical moves like blocking their path or surrounding them in a collapsing sphere, or any other sensible move that any competent combat captain would know and make.
