Launching a nail bomb into orbit would've been possible as soon as we were able to get into space, the only question is motivation. A terrorist state, say North Korea, threaten the rest of the planet and demand concessions once they're able to get any significant mass into orbit.
With GEO sats, unless you go for direct GEO insertion, it might still have issues reaching the final orbit. And even at GEO, there could be a debris cloud as well causing issues, at least until the sun and moon gravity perturbs it enough.
Not a satellite expert, but I understand GEO clears out relatively fast (~decades), because of those 3-body perturbations,
https://www.agi.com/blog/2020/07/geo-satellites-don-t-decay-...
It's new information to me, though. Thank you.
So unless somebody maliciously launches e.g. a bunch of ball bearings in the same orbital plane but opposite direction, the chances of "wrecking GEO" seem much lower (although the consequences would, as you say, probably be much more severe and long-term).
Targeted space junk disposal in GSOs appears to be quite practical. The easiest major orbital changes for an SEP stage to burn, structurally, involve lowering periapsis from high orbit.
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.