feat: add FastAPI backend with PostgreSQL and start script fixes

- Add server/ directory with FastAPI backend
- Fix server/start.sh to properly handle venv on Windows/Git Bash
- Add alembic migrations and pyproject.toml
- Add server tests

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

server/alembic/script.py.mako

@@ -0,0 +1,26 @@
+"""${message}
+
+Revision ID: ${up_revision}
+Revises: ${down_revision | comma,n}
+Create Date: ${create_date}
+"""
+from __future__ import annotations
+
+from alembic import op
+import sqlalchemy as sa
+${imports if imports else ""}
+
+
+# revision identifiers, used by Alembic.
+revision = ${repr(up_revision)}
+down_revision = ${repr(down_revision)}
+branch_labels = ${repr(branch_labels)}
+depends_on = ${repr(depends_on)}
+
+
+def upgrade() -> None:
+    ${upgrades if upgrades else "pass"}
+
+
+def downgrade() -> None:
+    ${downgrades if downgrades else "pass"}