Does an Eldritch Knight fighter’s War Magic feature benefit from the Extra Attack feature?


I am wondering about the wording here. On PHB p. 75, the description of the Eldritch Knight fighter’s War Magic feature says:

When you use your action to cast a cantrip, you can make one weapon attack as a bonus action.

Does the Eldritch Knight’s War Magic feature benefit from the Extra Attack feature, allowing them to make multiple attacks?

I feel like the wording would have to be "you can take an Attack action as a bonus action" to have access to multiple attacks. But the current wording doesn’t so I read this as not allowing multiple attacks.

Am I right, or does War Magic allow the Eldritch Knight to benefit from the "Extra Attack" feature too?