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/alembic/versions/520df92643e3_added_replypier_ai_model.py

@@ -0,0 +1,46 @@
+"""
+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.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+"""
+
+"""Added replypier AI model
+
+Revision ID: 520df92643e3
+Revises: 85364d188f15
+Create Date: 2025-03-28 23:27:11.906265
+
+"""
+from typing import Sequence, Union
+from alembic import op
+import sqlalchemy as sa
+from sqlalchemy.dialects import postgresql
+
+# revision identifiers, used by Alembic.
+revision: str = '520df92643e3'
+down_revision: Union[str, None] = '85364d188f15'
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+def upgrade() -> None:
+    # ### commands auto generated by Alembic - please adjust! ###
+    # Create a new temporary type with the new value
+    op.execute("ALTER TYPE aimodeltype ADD VALUE IF NOT EXISTS 'REPLYPIER'")
+    # ### end Alembic commands ###
+
+def downgrade() -> None:
+    # ### commands auto generated by Alembic - please adjust! ###
+    # Note: PostgreSQL does not support removing enum values
+    # We can only create a new enum without the value and replace the old one
+    pass
+    # ### end Alembic commands ###