Kessler syndrome relies on two key provisions:

1. Orbiting objects never try to avoid each other.

2. They're in high enough orbits that atmospheric drag is not a significant factor such that debris can last decades or centuries.

Starlink fails both as they constantly maneuver and they're in low orbits that are constantly cleaned by the atmosphere.

And I'd add that "kessler syndrome" is actually a statistical process, not a rapid sudden cascade of satellites crashing into each other. It takes years to decades for it to actually "happen". It's not something that can be caused by military action either.