Heroes 5.5 WarGame Edition - Tactical Edition.

Right now, for example, having both rapid fire and a tent is too much.

To make this particular combination work better than others, you need to have both a ballista and a tent simultaneously, and also need that healing when dealing damage, as well as have sufficiently high stats for the ballista (which is why rapid fire was chosen instead of crafting or plague tent, and why ballistics were chosen instead of artillery).
P.S. I specifically renamed the basic perks to avoid confusion with the machines themselves.

You still haven't answered the question of how many and which of your options will work effectively.
Machine Loyalty is a very weak and unappealing perk (since it has become a general perk, there will likely be no golems in the army). You invest in it instead of much stronger perks from the machinery tree. Furthermore, it is a basic and situational perk: it requires leadership to be effective. Will there be any additional bonuses? Will you have any bonuses for the dead catapult branch?
Because right now, I only see 2-3 build options according to your scheme: the entire catapult branch is dead, and the choice is only between a triple ballista and a double ballista + tent (plague tent is unappealing in the original - if you don't enhance the tent, since the ballista deals more damage and without sacrificing healing). Moreover, in all of them, there is a forced increase in initiative for machines (rune machines). That is, it is simply impossible to see a machinist without this perk. If the ballista or tent is strong, it will always have high initiative. Monotony.

Finally, your scheme has a drawback in the form of firearms. In combination with rapid fire, this is too powerful a perk. And since chaos is not guaranteed for the machinist, problems arise. Either the ballista shoots normally without firearms, and then the build with firearms is overpowered. Or the ballista shoots normally only with firearms, but then the build without it is pointless. There is too much difference between a ballista with and without firearms. Furthermore, firearms without machinery and a ballista perform much worse. Finally, let's say the hero has invested in chaos, but he has neither machinery nor a ballista. Why would he bother with perks like firearms and exorcism? He probably doesn't need it in most cases. Perhaps, so that he would refuse even the mana burst, which opens such a strange fork.

And another drawback of your scheme (and we are only discussing machines). This is ranged attack. It is a level 3 perk and competes with retribution. If you haven't weakened it, then retribution is a bomb perk that gives +10-25% damage to all troops (and not just ranged units). Therefore, ranged attack should be at least 50%. And then there is again a huge difference, a ballista with ranged attack and a ballista without. And what if it also has firearms at the same time? And if you add education to this + the dependence of the ballista on stats (which will be different for different races), then it turns out that the effectiveness of the ballista strongly depends on a large number of factors (race, education, machinery + rapid fire, firearms, ranged attack), which either add up to an overpowered build, or add up to a normal build, but are weak in other scenarios. Ah yes, there is also luck? Has it been reduced to +50% damage, as in WGE? Then we get another powerful factor.

How to build a super-machinist. Take Daleb, invest in firearms (6 levels), rapid fire (6 levels), ranged attack (6 levels), luck (3-6 levels and/or artifacts), education (3 levels). You get x2 damage for firearms, x3 for rapid fire, x1.5 for ranged attack, x1.5 for education, x1.5 for race (75% attack + knowledge vs. 50%) and a couple more for specialization (we won't calculate). You get a x20 modifier to ballista damage in the best case. If you add luck, then up to x30 or more (depending on the elf). Compare this to ordinary machinists who just invest in rapid fire (x3 modifier). Theoretically, of course, you can balance it so that, for example, starting from x10, the ballista will simply destroy any full stack in one volley, and then large upgrades will not be needed. But this will only partially solve the problem (the gap between 3 and 10 is still large).

What about the ballista in WGE. Ranged attack is only +30% (not that much). Firearms are in the machinery tree, and their bonuses are actually increased (and therefore they are effective separately), while they are not compatible with multi-shot (no overpowered build). Thus, firearms as a factor for a super-ballista is excluded (rapid fire is more powerful with high stats and ranged attack). The hero's race, education, and stats still significantly affect the strength of the ballista, but the balance can be adjusted for strong builds (because weak builds from the machinery tree will rather invest in artillery + firearms and be happy with just a good ballista, investing only 2 levels - 4 others in artillery).

And in your scheme: What to do with heroes who require basic perks like ballista (machinists) or tent (Kaspar)? What to do with other heroes whose specializations imply basic perks (like curse, beam, fireball, etc.)? Give them other basic perks at the start, so that they are then forced to invest in their own? I also considered the binary scheme from these positions and realized that it is not suitable for these criteria either.