Procedure for sous vide potato salad prep
Carrot and potato can work well using sous vide.  In fact, sous vide carrots are delicious.  Cook at 90C.  The issue will be timing, because it depends on the size of your veg.  You are just going to have to check them until you achieve the result you like.  Too long, and they will get mushy.  For me, a whole carrot usually takes 45 min to an hour.  So, a diced carrot could take substantially less time.  The same holds true for potatoes...thin slices can take less than 30 minutes, for example.

I have not done them myself, but I assume parsnip and celery root would behave similarly.  Use the same temperature, but time will have to be assessed as you go.

Additionally, all of these vegetables will float given that they contain a lot of air.  Vacuum sealing will help, but may not keep them under water, as air is expelled during cooking.  You will need to weigh down the bags or keep them submerged by placing something on top of them.

In the end, cooking them traditionally might just be the better way to go.