chore: settle product naming across app, widget and deployments

One word everywhere: ReplyPier in UI copy, package and image names, the
replypier.site domains (app/api/docs/help), REPLYPIER_* settings and the
--rp-* design tokens.

- public widget API is window.ReplyPier with replypierId / replypierBaseUrl /
  replypierConfig / replypierToken, loader at webclient/replypier.min.js;
  both bundles rebuilt from source
- NOTICE, llms.txt, CONTRIBUTING, HELP_CENTER_INFRA and the demo runtime
  config rewritten; the demo config ships no third-party keys
- migration adds the ReplyPier managed model value to the AI model enum
- local compose project, database, role, volume and Docker network carry the
  same name

backend/app/services/meta_own_app.py

@@ -1,5 +1,5 @@
 """
-Copyright 2024-2026 ChatterMate
+Copyright 2024-2026 ReplyPier
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
@@ -14,7 +14,7 @@ See the License for the specific language governing permissions and
 limitations under the License.
 
 WhatsApp numbers and Messenger Pages that live in the customer's own Meta
-app (connected with manual credentials) rather than in ChatterMate's.
+app (connected with manual credentials) rather than in ReplyPier's.
 
 Meta signs their webhooks with the customer's app secret, which the shared
 /webhooks/meta endpoint can't check. So each such account gets its own
@@ -95,7 +95,7 @@ async def resolve_own_app(access_token: str, entered_secret: Optional[str],
     """The customer's own app behind this token, proven with its secret —
     the one entered, or else the one kept from the last connect (checked
     again: the new token may be from another app). None without a secret, or
-    for ChatterMate's own app, whose webhooks the shared address already gets.
+    for ReplyPier's own app, whose webhooks the shared address already gets.
 
     Raises AppSecretMismatch or AppCheckUnavailable."""
     secret = entered_secret or (own_app_secret(previous) if previous is not None else None)