I've encountered this many many times including this spring.
If I do nothing, the potatoes will rebound with new growth, but the energy required to produce it will reduce your production (usually for me first time frost 10% reduction on short plants, second time about 25%). Happened to me this spring already and they all recovered fine...but I do expect a production hit. I have so many plants out with my experiment going, it was just too much trouble to protect them all.
However, I usually try to protect. If the plants are short like yours are, I will cover lightly with dirt entirely then the next day or so brush the dirt off to show green foliage. Like you mentioned you need the dirt anyway.
If the vines are medium to large, I have a frost plant cover for protection but that is a pain and I've never had to resort to that. Never had a frost that late in the cycle.
Good luck...anything else at risk in your garden?
p.s. here is the current potato stand which was frosted back to the ground in mid-March. Looks fully recovered...but there will be a price to pay at harvest.
View attachment 95574