>>13875724>>13877994will also mention that stars in the A, F, O range (Sirius on up) don't last beyond 500 million years. Their planets might get life at the end of those years, but that life is Precambrian.
Keep in mind these numbers:
Solar system: 4,567 million ya
Cryogenian: 720 mya
Ediocarian = Vendian: 600ish mya
Cambrian explosion: 541 mya
With this as guide, a mainseq star that goes red-giant after 4000 mya is a star that probably isn't a good target for a telescope looking for reasonably-advanced "life".
Interestingly, our own star as a G type is considered nonideal these days; cooler K types last longer. (M types tend to be flare stars and their planets are tidally locked; so too cool, and the planet is an irradiated airless desert, like Prox Centauri's inner planet.)