Rename billing to payment throughout the codebase (#726)

* Rename billing to payment throughout the codebase

This change updates terminology from "billing" to "payment" to better
reflect that these are contributions/payments rather than bills.

Changes include:
- Rename BillingsController to PaymentsController
- Rename billing_email to payment_email
- Rename next_billing_date to next_payment_date
- Rename create_billing_portal_session_url to create_payment_portal_session_url
- Update routes from billing to payment
- Update all 12 locale files with new terminology
- Update views, helpers, and tests

* Update app/views/subscriptions/upgrade.html.erb

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
Signed-off-by: Juan José Mata <jjmata@jjmata.com>

---------

Signed-off-by: Juan José Mata <jjmata@jjmata.com>
Co-authored-by: Claude <noreply@anthropic.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

test/controllers/subscriptions_controller_test.rb

@@ -44,7 +44,7 @@ class SubscriptionsControllerTest < ActionDispatch::IntegrationTest
     @mock_stripe.expects(:create_checkout_session).with(
       plan: "monthly",
       family_id: @family.id,
-      family_email: @family.billing_email,
+      family_email: @family.payment_email,
       success_url: success_subscription_url + "?session_id={CHECKOUT_SESSION_ID}",
       cancel_url: upgrade_subscription_url
     ).returns(