feat(chat): add random public_id and fix users blocked route

- add chats.public_id random identifier with migration 0011
- expose public_id in chat API payloads
- use chat public_id in message search UI label
- fix users router order so /users/blocked no longer conflicts with /users/{user_id}

alembic/versions/0011_chat_public_id.py

@@ -0,0 +1,43 @@
+"""add chats public_id
+
+Revision ID: 0011_chat_public_id
+Revises: 0010_blocked_users
+Create Date: 2026-03-08 15:00:00.000000
+"""
+
+from typing import Sequence, Union
+
+from alembic import op
+import sqlalchemy as sa
+
+from app.utils.id_generator import generate_public_id
+
+
+revision: str = "0011_chat_public_id"
+down_revision: Union[str, Sequence[str], None] = "0010_blocked_users"
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    op.add_column("chats", sa.Column("public_id", sa.String(length=24), nullable=True))
+    conn = op.get_bind()
+    rows = list(conn.execute(sa.text("SELECT id FROM chats")))
+    used: set[str] = set()
+    for row in rows:
+        chat_id = row[0]
+        public_id = generate_public_id()
+        while public_id in used:
+            public_id = generate_public_id()
+        used.add(public_id)
+        conn.execute(
+            sa.text("UPDATE chats SET public_id = :public_id WHERE id = :id"),
+            {"public_id": public_id, "id": chat_id},
+        )
+    op.alter_column("chats", "public_id", existing_type=sa.String(length=24), nullable=False)
+    op.create_index(op.f("ix_chats_public_id"), "chats", ["public_id"], unique=True)
+
+
+def downgrade() -> None:
+    op.drop_index(op.f("ix_chats_public_id"), table_name="chats")
+    op.drop_column("chats", "public_id")