There's another interpretation of this "casting time" conundrum. The cantrip replaces one of your attacks, but nowhere does it say that the casting time changes to a single action.
Round 1
Player: I make one attack with my rapier, and use my other attack to cast mending.
DM: Remember, mending has a casting time of one minute.
Player: Yep, that's right.
Round 2
Player: Okay, I make two attacks with my rapier.
DM: Remember, you're still casting mending. Do you wish to abandon that spell?
Player: Shoot, I forgot. I'll make one attack, and use my other attack to continue casting mending.
Would this mean that a Bladesinger using a bonus action cantrip as part of their attack is now locked out from casting any leveled spells with their actual bonus action?
I'm inclined to say no, as the rule states: "A spell cast with a bonus action is especially swift.
You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.". Since you're not using a bonus action to cast the cantrip as part of your attack, it seems like this should supersede that rule.
But if you're not using a standard action, bonus action, reaction, or anything else to cast this spell when you make an attack, it seems odd to argue about the casting time of the spell. The bladesinger casts the cantrip as part of their attack action. This replaces the normal casting time of the cantrip because it has to in order to function. If the normal casting time of the cantrip is replaced, then it shouldn't matter what the normal casting time is,
unless the ability itself tells us it does. We shouldn't have to go looking for "hidden rules" about "standard cantrip rules" (as Maxperson insists).
As I see it, as written, the Bladesinger's ability doesn't function because it doesn't grant any specific ability to do so. For example, if it said: "when you take the attack action, you can replace one of your attacks with a spellcasting (or to use the playtest parlance, a magic) action to cast a cantrip", we would know exactly how the rules interact with this ability.
It doesn't do that. Of course, we all know it's supposed to work, so we ignore any reading that says it doesn't work. But from this point on, it's all rulings, as we don't know what the intent was. A ruling that it is a spellcasting action, subject to all the restrictions thereby, or that it lets you cast the spell, waiving the normal action rules for doing so, are both equally valid.
However, Occam's Razor would suggest that the former ruling is likely the intended one, not the latter, so it's an acceptable ruling, but still, a ruling, not a rule. Because the rule is incomplete.
Here's a ludicrous analogy to my point.
The Pieslinger Subclass gains the ability, "when the Pieslinger takes the attack action, they throw a pie." What kind of pie? Do I need to furnish the pie, or does it just appear out of thin air? Do I need a free hand to throw the pie? Is this ability subject to the normal rules for throwing pies? Am I allowed to throw custard pies, even though the rules for pie throwing say "you cannot throw custard pies"? Can I throw cheesecake, even though my local Baker's Square insisted for decades that cheesecake is not a pie?.
