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/src/app/api/v1/endpoints/reimbursements.py

@@ -0,0 +1,31 @@
+from __future__ import annotations
+
+from typing import Annotated
+
+from fastapi import APIRouter, Depends, HTTPException, status
+from sqlalchemy.orm import Session
+
+from app.api.deps import get_db
+from app.schemas.reimbursement import ReimbursementCreate, ReimbursementRead
+from app.services.reimbursement import ReimbursementService
+
+router = APIRouter()
+DbSession = Annotated[Session, Depends(get_db)]
+
+
+@router.get("", response_model=list[ReimbursementRead])
+def list_reimbursements(db: DbSession) -> list[ReimbursementRead]:
+    return ReimbursementService(db).list_reimbursements()
+
+
+@router.post("", response_model=ReimbursementRead, status_code=status.HTTP_201_CREATED)
+def create_reimbursement(payload: ReimbursementCreate, db: DbSession) -> ReimbursementRead:
+    return ReimbursementService(db).create_reimbursement(payload)
+
+
+@router.get("/{request_id}", response_model=ReimbursementRead)
+def get_reimbursement(request_id: str, db: DbSession) -> ReimbursementRead:
+    request = ReimbursementService(db).get_reimbursement(request_id)
+    if request is None:
+        raise HTTPException(status_code=status.HTTP_404_NOT_FOUND, detail="Request not found")
+    return request