Does the sun have enough mass to go nova?
Absolutely it does. It doesn’t have enough to go supernova though.
When I took introductory astronomy back in the middle ages, they taught us that the Sun would "go nova" someday; i.e., blow off its outer layers and become a red giant. The whole process was referred to as "going nova." To an outside observer it will look like a new star (nova stella) has appeared in the sky.
But now most references on the web say a nova is white dwarf feeding on its red giant companion star. The gas flowing onto the surface of the white dwarf is hot enough that you actually get a massive nuclear explosion, or explosions, on the dwarf's surface. It's so bright it appears in the sky as a new star, but fades quickly until the next batch of gas explodes (Wow, this is something they never taught us).
Obviously, this will not happen to the sun because it doesn't have a companion, much less a white dwarf companion.
Thanks for the question (and the answer, Filo). You prompted me to go out and learn something new today! :-)