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/api/channels/meta.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.
@@ -302,7 +302,7 @@ def _upsert_account(db: Session, organization: Organization, channel_type: str,
                     forget: tuple = ()):
     """Create the account or refresh credentials on reconnect (same org only).
     `forget` names stored credentials that no longer apply (an app secret,
-    once the account is connected through ChatterMate's own app)."""
+    once the account is connected through ReplyPier's own app)."""
     repo = ChannelAccountRepository(db)
     existing = repo.get_by_external_id(channel_type, external_account_id)
     if existing is not None:
@@ -542,7 +542,7 @@ async def list_messenger_signup_pages(
     pages = await _list_manageable_pages(user_token, "id,name,access_token")
     if not pages:
         raise HTTPException(status_code=400, detail=(
-            "No Facebook Pages were shared with ChatterMate. Run the connect "
+            "No Facebook Pages were shared with ReplyPier. Run the connect "
             "again and tick the Page you want to use."))
 
     return MessengerSignupPagesOut(