You do not need to worry at all, as there are several everyday dairy and pantry items that will give you fantastic results without making your mashed potatoes feel lacking.
Sour cream is arguably the absolute best direct substitute for butter in mashed potatoes. It has a high fat content that delivers the velvety richness you expect from butter, while also adding enough moisture so you may not even need as much milk. It brings a gentle, pleasant tang that complements the earthiness of the potatoes wonderfully. You can start by adding a quarter cup for an average batch and adjust to your preferred consistency.
Another outstanding option is plain cream cheese. When melted into warm potatoes, it creates an exceptionally creamy, thick, and luxurious texture. If you decide to use cream cheese, let it soften at room temperature for a few minutes or cut it into small cubes before mashing so it incorporates smoothly.
If you prefer to avoid more dairy or want to use what is already in your cupboard, extra virgin olive oil works surprisingly well. While it will not taste like classic homestyle buttered potatoes, it lends a distinct, silky mouthfeel and a lovely fragrant aroma. Use a light hand, adding a tablespoon at a time so the flavor does not overpower the dish.
Finally, whole milk Greek yogurt or even a couple of tablespoons of real mayonnaise can step in if needed. Just remember to taste and adjust your salt and pepper as you go, since butter typically adds some seasoning that you will want to balance out.