Does Thirsting Blade Stack With Twinned Blades?

Question

Does Twinned Blades from the Compendium of Forgotten Secrets: Awakening stack with Thirsting Blade? Twinned Blades says both weapons are pact weapons, and Thirsting Blade affects my pact weapon. So can I make 4 attacks in a turn with these two invocations using plus 1 from Improved Pact Weapon and add my Strength Modifier to both attacks?

Here are the Twinned Blades Invocation from Compendium of Forgotten Secrets: Awakening and Thirsting Blade:

TWINNED BLADES

Prerequisite: Pact of the Blade feature

You gain access to a second pact weapon, and you can summon both whenever you would summon one of them. When you engage in two-weapon fighting using both your pact weapons, you can add your ability modifier to the damage of the bonus attack.

THIRSTING BLADE

Prerequisite: 5th level, Pact of the Blade feature

You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.

Answer 1

You would get three attacks total because Twinned Blades uses Two-Weapon Fighting and not the Attack action itself

What Thirsting Blade does, is it allows you to attack twice with your Pact Weapon when you take the Attack action. You are only taking one Attack action, so you only get the extra attack once.

What Twinned Blades lets you do is use Two-Weapon Fighting while adding a damage modifier. To quote Two-Weapon Fighting:

When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative. [...]

Two-Weapon Fighting involves making an attack but it does not involve the Attack action itself (for more on this distinction, we have: "What does upper-case-A-Attack action vs. lower-case-a-attack mean?"). Because the Twinned Blades Eldritch Invocation does not allow you to take a second Attack action, you cannot benefit from Thirsting Blade a second time. This gives you a grand total of three attacks (one from the Attack action, one from Thirsting Blade, and one from Two-Weapon Fighting).