Banks can settle with Visa and Mastercard in their currency of choice, so I don't see why the dollar matters for any of that.

And regarding Visa and Mastercard being US payment networks: This is now undoubtedly the case, but for much of their history, their EU subsidiaries were actually independent cooperatives owned by large European network member banks. They only sold their respective stakes to the US parent organizations in the late 90s, back when European banks, in a pretty severe blunder, considered cards a thing of the past of no importance for the future.