If you have purchased a ticket which originates or terminates in the US and a flight is cancelled, you are entitled to a refund. If you request one and it it is not initiated within 7 days, then you should dispute the charge with your credit card issuer (bank). Supply a copy of your e-ticket receipt, the cancellation notice, your request for a refund, and any denial of a refund (or a note from you that you have not heard back).

Don't try to come up with inapplicable analogies, don't try to parse through the law of agency, and don't worry about how the card issuer, the carrier, and the TA sort it out.

In future, do not book through TA's other than bricks & mortar operations where you have a direct personal relationship with staff and they have a reason to properly serve you. Those TA's likely charge fees and only you can determine whether the level of service makes the fee worth it.