refactor(billing): remove Stripe; payments are Payple (web) and Google Play (mobile)

Stripe is not used. Keeping its checkout, portal and webhook paths meant a
second payment provider, a second return-URL format and dead UI.

- Delete the stripe-checkout, stripe-portal and stripe-webhook functions and
  their config; billing-catalog serves Payple prices only, and the web parser
  rejects a catalog that still mixes in Stripe prices.
- Web: drop the Stripe checkout/portal buttons, provider toggle and return
  notices; billing shows Payple only. Past rows with provider='stripe' are
  still displayed ("Stripe (종료)") with a support contact instead of a portal.
- Desktop: delete the Stripe checkout modal, payment IPC channels, preload
  namespace and their types; "Remove ads with Pro" opens the web billing page
  via license.openBilling. Support/refund copy names Payple.
- billingUrl() loses the Stripe-only success/canceled result option; the
  Deno contract is regenerated.
- Migrations and the DB's accepted provider values are untouched (history).
- Docs and the backlog record the removal (MON-04, EXT-STRIPE-01, GAP-BILL-03).

Verified: typecheck (desktop/web/admin/api-client/mobile), contract:check,
deno check all functions, deno test 80/80, desktop 1478/1480 on the Electron
runtime (2 known environment failures), web and admin builds, release
metadata and mobile boundary self-tests, eslint on changed files.

scripts/capture-desktop-actual-app.js

@@ -202,22 +202,9 @@ async function capture() {
     await page.waitForTimeout(400);
   }
 
-  // 4. Click "Remove ads with Pro" on banner to show CheckoutModal
-  console.log('Capturing Screenshot 4: Checkout Modal...');
-  const removeAdsLink = page.locator('text=/Remove ads with Pro/').first();
-  if (await removeAdsLink.isVisible()) {
-    await removeAdsLink.click();
-    await page.waitForTimeout(800);
-    await page.screenshot({
-      path: path.join(SCREENSHOT_DIR, '14_actual_desktop_checkout_modal.png'),
-    });
-    await page.keyboard.press('Escape');
-    await page.waitForTimeout(400);
-  }
-
   await browser.close();
   server.close();
-  console.log('All 4 actual desktop app screenshots captured successfully!');
+  console.log('All 3 actual desktop app screenshots captured successfully!');
 }
 
 capture().catch((err) => {

scripts/ci/sync-core-contract.mjs

@@ -151,8 +151,8 @@ async function validateContract(source) {
   for (const [key, url] of Object.entries(contract.SITE_URLS ?? {})) {
     if (!String(url).startsWith(`${contract.PUBLIC_SITE_ORIGIN}/`)) fail(`SITE_URLS.${key} must live under PUBLIC_SITE_ORIGIN.`)
   }
-  const billing = contract.billingUrl({ tier: 'pro', result: 'success' })
-  if (billing !== `${contract.WEB_APP_URL}/billing?tier=pro&success=1`) {
+  const billing = contract.billingUrl({ tier: 'pro' })
+  if (billing !== `${contract.WEB_APP_URL}/billing?tier=pro`) {
     fail(`billingUrl() contract changed unexpectedly: ${billing}`)
   }
 }