Refactor process_payment and wc-stripe-is-deferred-intent flag

[ricardo]

The goal of this issue is to track this "To be removed" check:

woocommerce-gateway-stripe/includes/payment-methods/class-wc-stripe-upe-payment-gateway.php

Lines 679 to 682 in 50a0da1

	// Flag for using a deferred intent. To be removed.
	if ( ! empty( $_POST['wc-stripe-is-deferred-intent'] ) ) {
	return $this->process_payment_with_deferred_intent( $order_id );
	}

The $_POST['wc-stripe-is-deferred-intent'] parameter was introduced in #2935 and meant to be temporary.

Removing this flag also involves refactoring process_payment, and as a result from this issue, we expect a unified process_payment that works for both deferred and non-deferred intent payment methods and phases out any code paths that still consider old iterations like the no-longer supported unified Payment Element.

Additional context

#3805 (comment)