does this mean that stars might be a lot closer than we thought?
In some cases yes
25.67 trillion miles to Alpha Centauri.
There’s your starting point. You do the math, I’m not even going to try.
light is just an identifier of the existence of matter, it does not limit matters law of existence
how fast matter moves is matters business
What about the things in the passenger side mirror?
Depends on what your definition of “a lot” is. It might mean we are maybe a thousand or so miles closer to our sun or that alpha centauri is ten thousand miles closer.. (my numbers are just examples) either way space will remain prohibitively huge for interstellar travel.