The "stars" seen streaking by starships might actually be much, much smaller and closer objects, which might glowing due to interactions with the warp field of starshps.
And it is possible that only the plots, and none of the visuals of Star Trek productions are based on knowledge of the future sent back in time to our era. Thus none of the visuals in *star Trek might be what it "really" looks like.
The speed at which "stars" pass starships in various Star trek productions is way too fast.
"Stars" seem to move from ahead of the ship to behind in just a few seconds. The average separation between a star and its nearest neighbor in our part of the galaxy is about 5 light years.
Thus a starship appears to be travelling at least 5 light years in just a few seconds.
A light year is defined as the distance travelled by light during one Julian calendar year of 355.25 Earth days. There are 31,557,600 seconds in a Julian calendar year. So travelling at a speed of one light year per second would be travelling at 31,557,600 times the speed of light.
Since the galactic disc of the Milky Way Galaxy is about 100,000 light years in diameter, the greatest distance possible to travel within the galactic disc is about 100,000 light years. And it would take 100,000 seconds to travel 100,000 light years at a speed of 1 light year per second. That is 27.777 hours or 1.157 days.
The apparent speeds of starships vary greatly from episode to episode, showing that the writers rarely, if ever, tried to calculate the travel times from the distances and the official warp speeds.
But some episodes clearly showed that starships couldn't travel long distances as fast as the passing "stars" would indicate.
In TOS "By Any Other Name":
KIRK: What's the point of capturing my ship? Even at maximum warp, the Enterprise couldn't get to Andromeda galaxy for thousands of years.
ROJAN: Captain, we will modify its engines, in order to produce velocities far beyond the reach of your science. The journey between galaxies will take less than three hundred of your years
Spock Fascinating. Intergalactic travel requiring only three hundred years. That is a leap far beyond anything man has yet accomplished.
In TNG "Where No One Has Gone Before"
LAFORGE: Well, sir, according to these calculations, we've not only left our own galaxy, but passed through two others, ending up on the far side of Triangulum. The galaxy known as M Thirty Three.
PICARD: That's not possible. Data, what distance have we travelled?
DATA: Two million seven hundred thousand light years.
PICARD: I can't accept that.
DATA: You must, sir. Our comparisons show it to be completely accurate.
LAFORGE: And I calculate that at maximum warp, sir it would take over three hundred years to get home.
In TNG: "The Price"
DATA: The data from the Barzan's probe of the wormhole are quite impressive, Captain. The wormhole delivered the probe beyond the Denkiri Arm, in the Gamma Quadrant.
PICARD: It would take nearly a century at warp nine to cover that distance.
DATA: The same distance could be achieved in a matter of seconds through the wormhole.
DATA: According to the Barzan probe, we should be in the Gamma Quadrant but these readings clearly indicate we are nearly two hundred light years away in sector three five five six of the Delta Quadrant.>
LAFORGE: Damn it, Arridor, we're seventy thousand light years away from our ships. Come on, now. Follow us in. We'll lead you.
Furthermore, there are two entire Star Trek series based on the premise that 24th century starshisp can only travel about a thousand times the speed of light.
In "Emissary" the first episode of DS9, Sisko and Dax pass through a wormhole:
DAX: There is a star just under five light years away. No M-class planets Computer, identify closest star system.
COMPUTER: Idran, a ternary system consisting of twin O-type companion
SISKO: Idran? That can't be right.
DAX: Computer, basis of identification.
COMPUTER: Idran is based on the analysis conducted in the twenty-second century by the Quadros-One probe of the Gamma Quadrant.
SISKO: The Gamma Quadrant? Seventy thousand light years from Bajor? I'd say we just found our way into a wormhole.
IN "Battle LInes":
SISKO: The other side of the galaxy, to be precise. The Gamma quadrant is seventy thousand light years from Bajor. It would take our fastest starship over sixty seven years to get here.
In "Caretaker", the first episode of VOY, the starship Voyager is transported into the Delta Quadrant:
KIM: Captain, if these sensors are working, we're over seventy thousand light years from where we were. We're on the other side of the galaxy.
JANEWAY: You've taken us seventy thousand light years from our home. We have no way back unless you send us, and we won't leave without the others.
JANEWAY: We're alone in an uncharted part of the galaxy. We have already made some friends here, and some enemies. We have no idea of the dangers we're going to face, but one thing is clear. Both crews are going to have to work together if we're to survive. That's why Commander Chakotay and I have agreed that this should be one crew. A Starfleet crew. And as the only Starfleet vessel assigned to the Delta Quadrant, we'll continue to follow our directive to seek out new worlds and explore space. But our primary goal is clear. Even at maximum speeds, it would take seventy five years to reach the Federation, but I'm not willing to settle for that. There's another entity like the Caretaker out there somewhere who has the ability to get us there a lot faster. We'll be looking for her, and we'll be looking for wormholes, spatial rifts, or new technologies to help us. Somewhere along this journey, we'll find a way back. Mister Paris, set a course for home.
So the speeds necessary for the "stars" to zoom by starships at warp speeds would be thousands of times faster than the meximum speed consistent with the storylines of Star Trek: Deep Space Nine and Star Trek: Voyager.
A meteor is a trail of glowing super heated air left by a speck of space dust or small rock entering the upper atmopshere of Earth.
When a meteoroid, comet, or asteroid enters Earth's atmosphere at a speed typically in excess of 20 km/s (72,000 km/h; 45,000 mph), aerodynamic heating of that object produces a streak of light, both from the glowing object and the trail of glowing particles that it leaves in its wake. This phenomenon is called a meteor or "shooting star". Meteors typically become visible when they are about 100 km above sea level.
And some Star Trek fans think that the "stars" passing by during warp are actually much smaller and closer than stars, and are small nearby objects in interstellar space, which might be glowing as a result of interactions with the warp field of a starship.
And another way to think about the problem is to consider the frame story of Star Trek, explaining how knowledge of future events has traveled back in time to our era. Star Trek never had an official frame story and probably never will. So nobody knows how accurate and complete the knowledge of the future is. It is quite possible that only knowledge of the plots of episodes and movies has arrived in our time, and the visual look is created by present day persons. Thus all the visuals may be what modern people imagine star Trek looks like, and not what it really looks like.
Thus the images of "stars" streaking by a starship are just a visually impressive but mathematially inaccurate product of 20th and 21st century tr produciton and not a reality in the "real" star Trek.