Adding os.path.abspath to the send_file request fixes the issue for me by making the send_file request pull from the first folder location described in my question.

• project-folder
  • UPLOAD_FOLDER <-- here
  • web_app_folder
    • app.py

The second endpoint becomes:

@app.route('/get/<string:name>', methods=['GET'])
def get(name: str):
    saved_file: SavedFile = SavedFile.query.filter_by(filename=name).first()

    path = os.path.join(current_app.config['UPLOAD_FOLDER'], saved_file.filename)
    
    return send_file(os.path.abspath(path), as_attachment=True)