ASW – Alternative hero leveling.

My opinion has changed again...
By the way, siege engines deal additional fire damage. Chaos has a Fire Lord ;)

No, my opinion hasn't changed; you probably misunderstood it initially. I'm not against tying things together based on aesthetics if it's dictated by gameplay, not just aesthetics. And I'm against trying to force everything to fit an aesthetic, ignoring all other factors.

Have you checked if the damage from siege engines is equivalent to magical fire (reducing defense and pyrokinesis)? If so, there is an additional connection, but that doesn't negate the fact that this decision is bad from a gameplay perspective.
In practice, this will lead to:
1) Engineers without Chaos (or non-engineers) will complain that the ballista is too weak, or engineers with Chaos will have an overpowered ballista (depending on the base stats of the ballista). It's impossible to find a "golden mean" because of two variables and a huge range.
2) In Chaos, this perk will only clutter the upgrade path if there are no siege engines and, especially, if there isn't even a ballista.

On the other hand, if firearms are in the siege engine branch, what complaints can there be about the gameplay? And if it's also in the catapult branch, which solves the problem of the huge range of the engineer's and non-engineer's ballista, and also creates two alternative upgrade paths for the ballista (rate of fire OR firearms)? I don't see any downsides to the gameplay. Now about the connections:
1) The catapult branch is called Artillery - Sulfur Rain - Fire Arrows (there is an association in terms of out-of-game meaning, the development of siege technologies and fire projectiles).
2) Artillery and Sulfur Rain deal direct damage to enemy troops, in addition to enhancing the catapult only in siege battles, thus there is a connection in terms of the damage dealt by machines.

You can nitpick about the connections (it's a matter of personal opinion), but they do exist. We have: an objective improvement in gameplay + a subjective difference in determining which connections are sufficient and which are not. In my opinion, that's how the upgrade tree should be structured (objectivity in primary details and possible ambiguity in secondary details).

But we've already discussed these arguments; I'm just giving them as an example.