How to dissolve salt into mashed potatoes

Until the salt is dissolved, you will always have the problem of separate grains. It seems that your potatoes are not moist enough for it to happen on its own. And salt won't dissolve in fat.

My suggestion is to choose a liquid - and it can be water, if you insist on staying vegan, else dairy is the typical choice - and dissolve the salt in it. You don't need much, a teaspoonful may be enough. Once you have the salty liquid, mix a small amount of potatoes into the liquid until dispersed. Then add a bit more, repeat, using larger and larger portions of mashed potatoes, until all is mixed. This will give you an even dispersal of the salty taste.

I make both vegan, vegetarian (ovo/lacto), and standard mashed potatoes in a few different ways. My favourite way to add salt is to use seasoned stock or demi-glace. There are great vegan and vegetarian options here (including homemade).

You can also grind your salt (assuming it's kosher or sea salt) in a burr grinder, or crush it in a mortar and pestle. Alternative is to use pickling salt, which is ground extra finely to simplify the pickling process. Smaller grains will dissolve in the potatoes faster.

I've also seasoned garlic as it roasted, and included that with olive oil (instead of vegan or regular butter). Season roasted garlic is pretty tasty, and the heat + roasting does pretty well in dissolving the salt. I find that olive oil is pretty great in potatoes as a simpler alternative to any form of butter.

Add more salt to the water you boil the potatoes in, or generously salt the tops of the potatoes while they are in the steamer.

Just like pasta, the boiling water is one of the best ways to get flavor into the item.

Unlike pasta, with mashed potatoes you get the ability to add flavor later as you mash, so you can choose salty things to add if you weren't able to get enough salt into the potatoes while boiling.

It sounds like you're cooking with rock salt or salt flakes. Just use regular shaker salt. It tastes exactly the same (at least once you've mixed it up in the food) and it'll always be fine enough to mix in immediately.

Try heating the butter and truffle oil and add the salt to that. If it does not dissolve then no harm done. You can add additional water until the salt dissolves. Look for a vegan butter with high water content. Soy milk and other vegetable based milks have fairly high water content.

As pointed out in comments I am aware NaCl is does not dissolve in fat as fat is not polar. On the butter it is a package deal. The truffle oil needs to get mixed in so why not mix it in early and it will mix easier hot.

Or start with moister potatoes then cook off liquid to get to the desired moisture.

Not sure how your vegan butter is composed, but could you dissolve the salt into that first? Alternately, you could whiz your salt in a spice grinder or use a mortar and pestle to create a finer grind.