How long would the Earth last if the sun became a black hole?

[Manga Shoggoth]

Gravitationally, quite a long time - pretty much the same amount of mass would be anchoring the Earth in orbit.

For other things...

The shortest answer is "approximately 8 minutes", which is the time light would take to reach us from the sun.

If there are any radiation-based effects they will hit at the speed of light (Gamma rays and other photons) and shortly thereafter (for the very small bits that have rest mass).

If we survive that, we are looking at something simillar to the What If Earth got Kicked Out of the Solar System? Rogue Earth scenario described by Kurzgesagt (the relevent stuff starts around 3:58 - the first bit is discussing how the planet would be ejected).