How does the altered Extra Attack feature of the Bladesinger (Tasha's Cauldron version) interect with the Eldritch Knight Fighter's War Magic feature?

Question

The Extra Attack feature of the Bladesinger allows you to replace one of your weapon attacks with casting a cantrip. The Eldritch Knight's War Magic feature checks if you have "use[d] your action to cast a cantrip." Technically, you have used your action to cast a cantrip, or at least part of your action. Can an Eldritch Knight 7 / Bladesinger Wizard 6 make a weapon attack and cast a cantrip with Bladesinger's Extra Attack and then make a weapon attack as a bonus action with Eldritch Knight's War Magic?

For completeness, the features state the following:

Bladesinger's Extra Attack:

Starting at 6th level, you can attack twice, instead of once, whenever you take the Attack action on your turn. Moreover, you can cast one of your cantrips in place of one of those attacks.

Eldritch Knight's War Magic:

Beginning at 7th level, when you use your action to cast a cantrip, you can make one weapon attack as a bonus action.

Answer 1

There are two possible interpretations.

#1. War Magic requires the Cast a Spell action.

The first interpretation is that when War Magic says,

when you use your action to cast a cantrip,

it is referring to the "Cast a Spell" action. With this interpretation, War Magic would not be able to be used with the Bladesinger's Extra Attack cantrip, because that cantrip is cast as part of the Attack action, not the Cast a Spell action.

#2. War Magic requires casting a cantrip as part of any action.

This second interpretation is that "when you use your action to cast a cantrip", it means that you cast a cantrip as part of any action, not just the Cast a Spell action.

It's up to the DM, but I believe #1 is the correct interpretation.

Both of these interpretations seem valid, and so I must say this is a DM judgment call. But I, as a DM, would rule that #1 is the correct interpretation.

I would rule this way because "uses an action to cast a spell" seems to be defined as part of the "Cast a Spell" action:

Spellcasters such as wizards and clerics, as well as many monsters, have access to spells and can use them to great effect in combat. Each spell has a casting time, which specifies whether the caster must use an action, a reaction, minutes, or even hours to cast the spell. Casting a spell is, therefore, not necessarily an action. Most spells do have a casting time of 1 action, so a spellcaster often uses his or her action in combat to cast such a spell.

To me it seems that "casting a spell as part of an action" and "using an action to cast a spell" are different things. The Bladesinger isn't expending their action to cast the cantrip, they are expending an available attack to cast their cantrip. When you take the Cast a Spell action, you are expending your action to cast the cantrip.

But it seems reasonable to rule otherwise.

Answer 2

This should work

@ThomasMarkov presents the premise that casting a cantrip as part of your extra attack is distinctly separate from taking the Cast a Spell action. I agree.

However, we arrive at different destinations because of this.

In the same way that taking the "Cast a Spell" action is not achieved by casting a cantrip during your attack action, the condition "when you use your action to cast a cantrip" does not explicitly call for the Cast a Spell action- it simply calls for you to cast a cantrip while using your action.

RAW, your scenario fits this trigger, barring any errata that specifies an EK requires the cast a spell ACTION, rather than a cantrip using your action.