Add DM chat send/list endpoints: filter, rate limit, conversations (US-4)

Implements direct-message (DM) chat send and history endpoints:
- Migration 0011_add_dm_last_read.py (last_read_at on conversation_participants)
- Models updated in backend/app/models/chat.py
- Router in backend/app/routers/chat_dm.py:
  - POST /api/chat/dm/{user_id}/messages (send DM, filtered via TextFilter, rate-limited via Redis)
  - GET  /api/chat/dm/{user_id}/messages (paginated history, updates last_read_at)
  - GET  /api/chat/dm/conversations (conversations list, last message, unread count)
- Blocks enforced in both directions (cannot send to/from blocked users)
- Self-messaging prevented, peer exist check, auth required
- Integration tests in backend/tests/test_chat_dm.py

Independently re-verified: 14/14 new DM chat tests pass,
272/272 full backend regression suite passes with zero regressions.

backend/alembic/versions/0011_add_dm_last_read.py

@@ -0,0 +1,36 @@
+"""add last_read_at to conversation_participants (DM unread tracking)
+
+Revision ID: 0011_add_dm_last_read
+Revises: 0010_add_profile_tables
+Create Date: 2026-09-15 00:00:00.000000
+
+app/routers/chat_dm.py (DM send/list/conversations endpoints). Unread-count
+tracking is implemented as a last-read timestamp per participant: whenever a
+user fetches a conversation's message history, their
+``conversation_participants`` row's ``last_read_at`` is bumped to "now", and
+the conversation-list endpoint counts messages with
+``created_at > last_read_at`` (or all messages if never read) as unread for
+that participant. Nullable/no default so existing rows (none yet in
+practice, but consistent with "never read") read as "everything unread".
+"""
+from typing import Sequence, Union
+
+from alembic import op
+import sqlalchemy as sa
+
+# revision identifiers, used by Alembic.
+revision: str = "0011_add_dm_last_read"
+down_revision: Union[str, None] = "0010_add_profile_tables"
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    op.add_column(
+        "conversation_participants",
+        sa.Column("last_read_at", sa.DateTime(timezone=True), nullable=True),
+    )
+
+
+def downgrade() -> None:
+    op.drop_column("conversation_participants", "last_read_at")