Please read or listen to Fauci's comments in full before going too far with it.
The way we can track long-term immunity is based on two things. 1) how long does your body maintain antibodies against the pathogen, and 2) how quickly does the pathogen mutate.
1) For many things, our bodies maintain antibodies lifelong, but for others we need boosters to keep our body primed. We need to deploy more tests (and we need more time) to see how our body's immune response to COVID persists over time. But, assuming we have antibodies, we should be protected from re-infection by the same virus. (The caveat is that an over-aggressive response by a primed immune system can also lead to problems). Based on similar coronaviruses, it seems like the body should mount an immune response that persists for a while.
2) Some pathogens don't mutate much, and thus we can develop a one-time vaccine for them, like smallpox. Others, like the flu, mutate every year, so we have to give seasonal vaccines. Others, like the common cold, is actually a broad class that encompasses many different types of viruses, and each of those mutates a lot, so a vaccine is not feasible. As for COVID, it appears it hasn't mutated much, which is encouraging and means we should be able to make a vaccine that is effective for years to come.
Fauci is using those two bits of information (one, that we see antibodies against COVID and that we see immunity built against similar viruses and two, that it hasn't mutated much) to say that we should have immunity against reinfection and that we should be able to design an effective vaccine. However, we still need more data, we need to understand why people are reinfected (did they not mount a strong antibody response? where they really reinfected or did they never clear COVID to begin wtih?), how long and robust are immune response is, and of course can we make a vaccine that is safe and effective.