running into range with this weapon while holding the fire botton results with a beam showing, but no damage being done, and since it disabled movement completely, you can't get the one pixel closer you need to start hitting. Even a tiny bit closer is enough.

Can you give sniper a VERY SLOW movement speed, rather than no speed at all?

In contrast to assault rifle, battle rifle, marksman rifle (and other types of rifles), sniper rifle is meant to be completely stationary (crawling or at least kneeling) to get the aim. Run-and-gun is no way for a sniper rifle.
I set it this way, not wanting players just use it like yet-another submachine gun / shotgun but with range advantage.

Maybe I should buff its range (to fight against the ridiculous long-ranged behemoth worm...).
Is it better than allowing a movement?

I'm not saying that it should be full run and gun thing, I'm saying that absolutly no movement cause it to bug at the edge range, inflicting no damage.
giving it a crawl pace movement should eliminate that issue (since you'll be able to step foward that last step to enter the range), and should also fix the footstep spam that it creates while trying to move while shooting.

Also, FYI, there's no speed penalty while flying with jetpack for any weapon.

Alright, adding a bit "crawl speed" does not hurt the sniper role play. I will adjust it when I have time.

I do not know jetpack, but I do know some mods are specifically removing all cooldown movement restrictions from all guns.
If players prefer OPness over balance, they are free to do so.

Just added the "crawl speed" together with other buffs to the laser sniper rifle in 0.17.14 / 0.18.3 / 1.0.0.