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/domain_verification.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.
@@ -16,7 +16,7 @@ limitations under the License.
 Custom-domain verification for the public help center.
 
 The customer proves control of the domain with a TXT record
-(_chattermate.<domain> = cm-verify=<token>) and routes traffic with a CNAME
+(_replypier.<domain> = rp-verify=<token>) and routes traffic with a CNAME
 to HELP_CENTER_CNAME_TARGET (A/AAAA records matching HELP_CENTER_TARGET_IPS
 are accepted for providers that flatten CNAMEs). Both must pass before the
 host dispatcher will ever serve the domain. SSL turns active once an HTTPS
@@ -38,7 +38,7 @@ logger = get_logger(__name__)
 
 DNS_LIFETIME_SECONDS = 5.0
 SSL_PROBE_TIMEOUT_SECONDS = 10.0
-TXT_RECORD_PREFIX = "_chattermate"
+TXT_RECORD_PREFIX = "_replypier"
 # Public resolvers for verification lookups. The container's own resolver is
 # Docker's embedded DNS (127.0.0.11) for service discovery — it negatively
 # caches names that didn't exist when first queried (so a TXT added *after* the
@@ -60,7 +60,7 @@ def txt_record_host(domain: str) -> str:
 
 
 def expected_txt_value(row: HelpCenterSettings) -> str:
-    return f"cm-verify={row.domain_verification_token}"
+    return f"rp-verify={row.domain_verification_token}"
 
 
 def _resolver():