As you can see, I have a pixel art of mountains. I would like to increase the quality of it (by quality, I mean less-pixelated look), is there an automatic way to do it in Aseprite, or is the only way to do it is to redraw it with smaller-sized brush?
In pixel art, brush size doesn’t really make anything more or less pixelated. Everything is pixelated regardless. The only thing that would make it less pixelated is increasing the resolution of the game itself, or smoothing the edges with more colors.
You can use
Scale.lua script from NxPA Studio scripts pack (look here) to enhance your mountains resolution 2x.
Or if you want more realistic look I suggest you ask for community for some auto-shading scripts to add lighting. Maybe those scripts could even use sprite brush (Ctrl+B) as pattern source.