If you join the jamaa as they are in the sujud of the first rakah, have you also completed the rakah? From what moment do you miss a rakah if joining salah later?

No, you did not complete this rak'ah; you have missed it. Therefore, after they finish and say, "Assalamu alaikum wa rahmatullah, assalamu alaikum wa rahmatullah," you get up and you pray one more rak'ah. The rak'ah is only counted for you if you make ruku' while they are still in ruku'. Before he says, "Sami' Allahu liman hamidah," then this rak'ah counts for you.