Quote a monthly private lesson per lesson, a group class monthly

A monthly charge covers every lesson that falls in the month, so a private
lesson's fee reads "50.00 CAD per lesson monthly" — the figure on its own would
suggest the whole month costs 50.00. A group class is enrolled in once, as a
single schedule, so its price is quoted as the monthly figure it is.

The pay agreement follows the same split: per-lesson for a monthly private
lesson, the monthly figure for a monthly group class. Weekly, full-term and
at-booking wording is unchanged.

Co-Authored-By: Claude Opus 5 <[email protected]>

docs/features/payments.md

@@ -102,16 +102,30 @@ After booking, the destination on a payment can be corrected per booking:
 Every price a student is shown on the front end carries its **cadence** — the
 offering's `billing_mode` in the words the student needs:
 
-| `billing_mode` | Shown as     | Explained beneath as                                       |
-|----------------|--------------|------------------------------------------------------------|
-| `one_time`     | `at booking` | Charged once, when you book.                               |
-| `full_term`    | `up front`   | Charged once, up front, for the whole term.                |
-| `weekly`       | `weekly`     | Charged for each lesson, 24 hours before it starts.        |
-| `monthly`      | `monthly`    | Charged on the 1st of each month, for that month's lessons.|
+| `billing_mode` | Shown as                          | Explained beneath as                                       |
+|----------------|-----------------------------------|------------------------------------------------------------|
+| `one_time`     | `at booking`                      | Charged once, when you book.                               |
+| `full_term`    | `up front`                        | Charged once, up front, for the whole term.                |
+| `weekly`       | `weekly`                          | Charged for each lesson, 24 hours before it starts.        |
+| `monthly`      | `per lesson monthly` / `monthly`  | Charged on the 1st of each month, for that month's lessons.|
 
 So a lesson type reads `50.00 CAD at booking` in the booking form's type picker,
 and a group class card reads `120.00 CAD up front`. A free offering shows `Free`.
 
+**`monthly` reads differently per offering kind.** A private lesson's monthly
+charge is that month's lessons × the fee, so the fee is quoted **per lesson**
+(`50.00 CAD per lesson monthly`). A group class is enrolled in once, as one
+schedule, so its figure is quoted as it stands (`120.00 CAD monthly`) — see
+`isPerLessonMonthly()` in `assets/js/pricing.js`.
+
+> **Caveat.** `ScheduledBillingRunner::billGroupMonthly()` bills a monthly group
+> class `price × sessions in the month`, the same per-session multiplication used
+> for private lessons — so a class meeting weekly is charged roughly four times
+> the quoted `120.00 CAD monthly` figure. The display deliberately quotes the
+> price as a monthly figure; closing the gap means either billing a monthly group
+> class once per month regardless of session count, or restoring the per-lesson
+> wording for group classes too.
+
 Before a booking or enrolment can be submitted, the form shows the price again as
 a summary block with a **required agreement checkbox** — the second confirmation,
 distinct from the policy acceptances above it:
@@ -133,6 +147,8 @@ Cadence-specific wording:
   simply not claimed, so the real charge can come in under it.
 - **`weekly` / `monthly`** — nothing is taken at registration, so the agreement is
   to the recurring charge: "I agree to pay 56.50 CAD per lesson, billed monthly."
+  A monthly **group class** agrees to its monthly figure instead ("I agree to pay
+  138.00 CAD monthly."), matching how its price is quoted on the card.
 
 All of this lives in `assets/js/pricing.js` (`window.usPricing`), shared by the
 booking and group-class flows so a price reads the same wherever it is met. The