next-intl Message Catalog and Locale Routing

Set up locale routing and a message catalog. Strings live in messages, not in components. A missing key fails the build or the test. APP Framework: [NEXT.JS APP ROUTER] Locales: [LIST] Default locale and whether it is prefixed: [en, PREFIX OR NOT] What moves into messages first: [NAV, AUTH SCREENS, EMAILS OR NOT] Formatting: [DATES, NUMBERS, CURRENCY] DELIVER 1) The route shape and the middleware or proxy that picks the locale. How a user switches and how we remember it. 2) The JSON catalog structure, one namespace per area, and the typed hook or helper. 3) A plural example and a rich-text example that does not concatenate sentences (translators need whole strings). 4) The test or typecheck that fails when a key used in code is absent in a locale, and when a locale has an extra unused key. 5) What stays out of the catalog: error codes from the server, log lines, names of flags. 6) Dates and currency formatted with the locale, not with a hardcoded MM/DD. Do not build the translated copy. Build the plumbing and five example strings that show the rules.