Haste gives you an attack action. It is a real attack action where you can do whatever you want.
Except in no case whatsoever can you make more than 1 attack in it.
If you are making a 2nd attack in that hasted action, then the 2nd attack never happens.
You can use your "Extra attack" feature, or any other feature, but any attack beyond the first in the action simply doesn't happen.
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Alternative reading is that you can take the attack action, but the only thing that attack action can contain is a single weapon attack. Nothing else. No nose picking, no free actions, nothing. This is slightly more strict than my reading above.
Given the spell casting rules in general, I'd say that a bladesinger couldn't use it for a cantrip if he had already done so as part of his regular attack action.
There is no limit to how many or what kind of spells you can cast with actions.
The rule is very narrow. If you use a bonus action to cast a spell, you cannot have cast any other spells this turn except a cantrip with a casting time of 1 action.
This is a rule for casting a spell with a bonus action. You can action surge and cast 2 spells, you can cast an action spell and a reaction spell
You cannot cast a bonus action spell and a reaction spell. You cannot cast a bonus action cantrip and a non-bonus action spell.
Arguably, you cannot cast a bonus action spell and cast a cantrip as part of an attack action, because that cantrip no longer has a casting time of 1 action.
You can action surge, attack + cantrip, attack+cantrip. And,
arguably, you can hasted action attack plus a cantrip that does not involve an attack.