Bonus Actions Are Actions? Combining Two Weapon Fighting and Extra Attack (Newly Expanded) [closed]

Let me first start by clarifying, I believe there is a point that has been missed in this question before. Consider that before marking it a repeat:

What is the precise differentiation between a bonus action and an action?

I believe that the combination of two weapon fighting and Extra Attack (granted at Level 5 Paladin) allows for a total of 4 attacks. Can anyone confirm this? Let me outline.

Extra attack: “Beginning at 5th Level, you can attack twice, instead of once, whenever you take the Attack action on your turn.”

Two Weapon Fighting: “…you can use a bonus action to attack with a different light melee weapon…”.

Most answers I’ve seen say three attacks, i.e. You get the Attack Action, which includes 2 attacks, and the bonus Action which includes 1 attack.

However, I believe the correct breakdown is first to thinking You get the Attack Action, which grants a Bonus Action (Attack Action). Now both of these Attack Actions should benefit from Extra Attack, giving 4 (lower case a) attacks within 2 (upper case A) Attack Actions. Thoughts?

The rules seem clear, that a bonus action is an action. And an action used to attack is an attack action. Thus, a bonus action used to attack is an attack action.

If this is not the case, where is there a clear distinction between bonus action and action?