I've read the rules quite extensively and will try to compile an answer to my own question.
No, they can't be used for those skills.
Siege Equipment are objects, not weapons.
They are classified as Large Objects, not weapons. Despite being occasionally referred to as "weapons", they don't fall under the category of Weapons, in the sense they can be equipped, disarmed and, above all, used in an Attack Action.
They don't require proficiency to be used
Your class grants proficiency in certain weapons,
reflecting both the class's focus and the tools you are
most likely to use.
Usually something like: proficiency with martial weapons, proficiency with swords. Siege weapons are usable by anyone, with the Use an Object action.
They are not listed in the weapons tables
Instead, they show up in the DMG, together with objects like Suspended Cauldrons. These cauldrons, despite being siege weapons (defensive mostly), are clearly not weapons in the regular sense, they don't even have an attack roll.
The PHB claims the table mentions only most common weapons, but these weapons all share many characteristics (which are also shared by improvised weapons):
they can be equipped and disarmed.
you add your own modifiers to their attacks
you use the Attack action to attack with them
they are neatly arranged into categories
We will see that Siege Weapons have none of these traits.
They have fixed damage and attack rolls
You don't add modifiers to them (Proficiency, Strength or Dexterity), either to Attack or Damage rolls. This is because it's the Siege Weapon's Attack Roll, and not yours.
They require actions to be used (not Attack Action).
It takes one action to load the weapon, one action to aim it,
and one action to fire it.
Meaning Extra Attack or similar features are off the table as well. Meaning anyone can use them, no proficiency with it is necessary.
When an object requires your action for its use, you take the Use an Object action.
So, you are not making the attack rolls at all, you are Using an Object, and the object's use has an Attack and a Damage roll. You fire the weapon (using the "Use an Object" action), and it's the object's attack roll (not yours). This also furthers the point that Siege Weapons are Objects you use, not Weapons in the classical sense.
Weapons belong to a class of weapons: simple or martial or natural, ranged or melee
Every weapon is classified as either melee or ranged.
The three categories are simple, martial, and natural.
This is supported by Crawford
There are three categories of weapons in the game:
A weapon is in only one of those categories, unless a rule makes an exception
No siege weapon is actually defined as belonging to any of theses classes. In fact, some would be quite hard to describe (Suspended Cauldron drops something on top of enemies, is this a ranged attack?).
Doval's comment also makes a great point:
Being able to make a ranged weapon attack doesn't make something a ranged weapon.
Now, let's closely examine each of the skills we looked at.
Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.
It requires ranged or finesse weapons, which Siege weapons are not (they are objects). You are also not attacking, you're using an object. You couldn't trigger Sneak Attack with a magical staff that threw a fire bolt at someone when used.
Flavor-wise, Sneak Attack is about using finesse to hit the soft-spots of a distracted target. It doesn't sound right to do this with a gigantic trebuchet, does it?
You gain a +2 bonus to attack rolls you make with ranged weapons.
Like before, siege weapons are not ranged weapons (just like you wouldn't get a +2 when throwing a Spear).
Plus, I still defend that you are not the one making the Attack Roll, as you don't add any modifiers to it. You are using an object, and its the object's attack roll, not yours.
you learn a ritual that creates a magical bond between yourself and one weapon.
These are not classical weapons, but Objects. You wouldn't be able to bond with a table, just because you can throw it at people. Just because you can use it as a weapon, it doesn't mean it IS a weapon. Also,
you can't be disarmed of that weapon unless you are incapacitated.
This implies you can equip a weapon and be disarmed from it, which does not happen with Siege Weapons.