You can only draw one weapon per turn for free
The rules state:
You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.
When you take the Attack action, you can draw a single weapon as part of that same action. Note how the rules specifically says "one object" and "your weapon". Also the sentence directly following this passage makes this more explicit:
If you want to interact with a second object, you need to use your
action. Some magic items and other special objects always require an
action to use, as stated in their descriptions.
Drawing one weapon is one interaction with one object. Trying to draw the second weapon would be a second interaction with a second object and thus it would require another action to perform.
Note that Extra Attack only adds attacks to a single Attack action, but the rule do not care how many attacks you are making, because you can only take one free interaction per action and only one per turn.