[T-hawk]

Short answer: recovering from Covid-19 probably does give immunity, based on all the precedents you mention, but we can't prove it for sure yet because not enough time has elapsed and no sufficiently rigorous studies have been done.

Of course viral antibodies persist for some amount of time, they don't disappear immediately upon clearing the virus. What we don't know is anything about the shape of that persistence. Is it days or weeks or years? Does it decline linearly, or exponentially (as a half-life), or on some other schedule? What kind of variance between people is there? How much does it vary based on all the other factors, like other health and immunological conditions, or re-exposure to the virus? This is all what we don't know yet, but need to before we can make assumptions regarding herd immunity to start lifting lockdowns.