Use new FastAPI CLI for development

[taesungh]

Following from #384, FastAPI 0.111.0 includes a new FastAPI CLI to make running the development server easier. Sample usage has already been integrated into the HackAtUCI/starter-pack-full-stack-web-app, and we can use it for this project as well.

• Update the requirements files to include fastapi-cli as a dev dependency
  • Note: do not use fastapi[standard] since the additional dependencies do not need to be bundled in the Vercel Serverless Function deployment (see explanation in Configure deploying full-stack app on Vercel starter-pack-full-stack-web-app#19)
• Update the API README file and Dockerfile with the new CLI commands
• Remove the dev.py script