Intercept payment method change

I am working on a custom extension where I need to call an observer when any payment method is selected from the available payment method list on the frontend checkout page.

Unfortunately, I didn’t find one, but it seems that I rather need to subscribe to quote.paymentMethod.

Can anyone tell me if there is an event for this that could be observed or should I subscribe to quote.paymentMethod?

PS. I need to recalculate the totals/save the quote once a payment method is selected.