Is Kessler syndrome the Great Filter (https://en.wikipedia.org/wiki/Great_Filter)?
As in, is it the thing that makes it so no one else has broken out of their planet to come visit us?
I could totally see it being the case that as soon as a civilization gets good enough at putting stuff into space, they start putting a lot of stuff into space and then things start crashing into each other to the point that they can’t ever launch any more things into space and become stuck. Trapped by the artifacts of their own progress
I'd consider it much less likely than e.g. nuclear or maybe chemical/biological warfare.
Kessler syndrome (if even achievable with current technology) would be a major bummer for science and the global economy for a couple of decades (no more Starlink, but we still have good old geostationary satellites, so no ships and airplanes would get disconnected as a result), or at worst centuries, but would otherwise not form any threat to civilization, whereas nuclear winter is already very capable of wiping it out.
I would guess that it would still be possible to send things beyond earth's orbit with only a low probability of collision with debris but perhaps I'm wrong.
No. The space junk at a given orbit makes it unviable to put more satellites in that orbit, but launching beyond that orbit is still viable.