mellored
Legend
No it doesn't.This does not work for several reasons.
Let's say you are an EK11/Bladesinger 6/Warlock 2
You can only use one version of extra attack. The game is specific about this.
Extra Attack
If you gain the Extra Attack feature from more than one class, the features don’t stack.
When you take the Attack action on your turn, you can replace one of the attacks with a casting of one of your Wizard cantrips that has a casting time of an action.
You can attack twice instead of once whenever you take the Attack action on you turn.
In addition, you can cast one of your cantrip that has a casting time of an action in place of one of those attacks.
They are not separate actions. It's just the attack action.
It's not a status.Multiple effects that cause the same status do not stack.
Going by your reading, you would not be able to use 2 unarmed stikes.
Now, you could add another rule in the EK saying it doesn't stack with similar features. But that's not in there by default.