if you sign the contract (click I agree on Terms of Service), and it says that they do not train on the data, by what right can they backtrack on that?

Maybe it is assumed that they notified you and you have the right to terminate the contract? Relying on some clause where the contract can be updated at any time. Or terminated at any time (with the presumption that a clause change is a termination and an automatic signing of the new contract, but that's weak)

Got to love the private equity parasites ruining everything for the sake of profit.