Add unread message indicators for rooms (#38)

Shows a dot on rooms with unread messages in the sidebar, updated live
over WebSocket. Reuses the same offline-member audience computation
already used for push notifications: a member gets the real-time signal
whenever they aren't currently connected to that room's channel, which
correctly covers both "room not open" and "room open but tab
backgrounded" (the client leaves a room's channel while hidden).

Persisted server-side via a new room_memberships.last_read_at column so
state survives reload and stays consistent across devices, advanced by
an explicit mark-read call the frontend makes on room-open and on each
live message received while the room is genuinely visible -- gated on a
live visibility check, not a cached ref, so a backgrounded-but-open room
keeps accumulating unread instead of auto-marking-read the instant a
message arrives somewhere it can't be seen.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/alembic/versions/f9eff917e5b3_room_membership_last_read_at_for_unread_.py

@@ -0,0 +1,32 @@
+"""room membership last_read_at for unread indicators
+
+Revision ID: f9eff917e5b3
+Revises: f0f6e494454a
+Create Date: 2026-08-16 20:14:32.449934
+
+"""
+from typing import Sequence, Union
+
+from alembic import op
+import sqlalchemy as sa
+
+
+# revision identifiers, used by Alembic.
+revision: str = 'f9eff917e5b3'
+down_revision: Union[str, Sequence[str], None] = 'f0f6e494454a'
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    """Upgrade schema."""
+    # ### commands auto generated by Alembic - please adjust! ###
+    op.add_column('room_memberships', sa.Column('last_read_at', sa.DateTime(timezone=True), server_default=sa.text('now()'), nullable=False))
+    # ### end Alembic commands ###
+
+
+def downgrade() -> None:
+    """Downgrade schema."""
+    # ### commands auto generated by Alembic - please adjust! ###
+    op.drop_column('room_memberships', 'last_read_at')
+    # ### end Alembic commands ###