How much value does Bloomberg provide on your resume when switching jobs? I'm guessing you'd still be able to get interviews with Google, but what about companies like LinkedIn, Uber, Airbnb, and Pinterest? Do they only give interviews to people from FNG or tier 1 unicorns? Would working at Bloomberg limit your job opportunities when you want to leave?
Safe to say no company limits your chances of interviews at another company. It is (and should be) your actual skills that you are judged on, and the quality of your experience, which doesn’t matter as much as you think which company you are at. Don’t forget it’s a very good job market for SDEs, so there is a major shortage of quality SDEs for the number of openings. Sure it helps to be at FNG, but it is never a requirement. Welcome to the real world!