When astronauts are floating about in a spaceship or space station, they nearly always move very slowly. After doing a bit of research I can't see why being in zero gravity would restrict movement to such a degree. It's almost as if there's resistance to their movement, like they're moving through water.
It's more for safety than anything else. Space is a very dangerous place for so many reasons. And making mistakes can very easily cause death.
Being weightless does not mean you lose mass, so momentum is just as difficult as ever. But whereas on the ground you can easily use friction to stop, in space if you try to stop against the floor you will just move off it. You can only stop by holding something, or pressing against something close to perpendicular to your movement.
As an example, imagine you jumped with all your force from one wall in the ISS. You will notice as you approach the other end that you are travelling at speed, head first, with no safe way to stop. Even reaching out to a handhold on a side wall will whip you round and into that wall, possibly injuring yourself or damaging instruments on the wall.
Look at any video from the ISS to see how carefully they move.
Similarly, outside the ISS, you want to do everything slowly so you don't damage your suit, miss a handhold or otherwise cause death.
Creating the illusion of weightlessness in movies actually requires a LOT of people operating cranes with harnesses and wires to hold the actors suspended in air. It's not easy moving (nor safe) the equipment holding the actors about as fast as real astronauts are able to move on the ISS. Also, it's important to not let the cranes and their crews fall into the view of the camera. As a result, there's quite a lot of choreography that goes into setting up weightless scenes, deciding the best camera angles, moving the actors, rehearsals, etc. All those factors go into slowing down the action we see in movies. Surprisingly, the wires are easier to hide either because their coloring and thickness are taken advantage of which causes them to be naturally hidden by the film's resolution in older movies, or they can be digitally masked out in post-production if needed in modern films.
Mind you, astronauts don't fly about helterskelter on the ISS! They're being very careful, there, too. But moving about the station only needs a very slight push off a wall and the same force to stop them when they get to where they want to be in very short time. But while they're flying between, they'll frequently entertain themselves doing stunts in zeroG such as flips and twists.
There is no air resistance in space. So if you increment your own speed you'll continue with that speed until you crash (considering the laws of thermodynamics).
For safety, you should move slowly.