Yes, it's still beneficial "to still continue taking muscle, energy, and endurance increasing supplements while cutting". No, using such supplements will NOT prolong your fat loss. And no, there is not "a specific kind of preworkout supplement made for cutting that isn't necessarily a 'fat burner'", but there are several preworkout products that will aid in fat loss, such as RPM and Anadraulic State.
I see no reason why you cannot use preworkout products when cutting. If anything, since most people generally reduce their caloric and/or carbohydrate intake ridiculously when cutting, then such supplements would actually be beneficial for energy, IMO!
~Rosie
Team APPNUT