I imagine they knew that Netflix was in talks to pick up seasons 1 and 2 for streaming as part of the wider AMC deal they announced recently, which gave them confidence that AMC would green-light another season.
As for why it would be season 3 and not its own thing, the blurb they released for season 3 would seem to indicate that Louis, Armand and Malloy will still be in the show and they would like to keep the momentum going that they have built with the first two seasons. Especially since the show has 2 spinoffs already.
“Resentful of the perfunctory portrayal in the trashy best-seller Interview With the Vampire, the Vampire Lestat sets his story straight in a way only the Vampire Lestat can — by starting a band and going on tour. Gabrielle. Nicholas. Magnus. Marius. Those Who Must Be Kept. They join Louis, Armand, Molloy, Sam, Raglan, Fareed and others we can’t tell you about yet on a sexy pilgrimage across space, time and trauma. No Auto-Tuning. No Trigger Warnings. All Feels Amplified.”