What kind of rendering are you hoping to achieve?
There’s a thread by @KnightsofFriendship, who used to take submitted screenshots (as well as some of their own), and “pretty them up” in Photoshop with stunning results. I’ll have a quick search around for their thread, it mentioned some of the techniques used in the process and might be a good place to get inspiration. No voxel/modelling program needed, just a little bit of Photoshop wizardry. Here is is: I take Photoshop requests
Alternatively, there’s “full renders” in the style of @Pandemic’s work (which is probably something you’ve seen around): Pandemic's Art and Modding Corner! Bringing Pretty Back since 2017! although this stuff is mostly built from scratch in modelling software or using in-game models (i.e. the model files that ship with the game) and loading them up into said software to create scenes.
Working with the voxel files of just the blocks used in buildings (i.e. the old “dump” method – although it’s unclear whether that still works) will give you only a part of the image; you’d need to re-add the terrain and furniture and so on. If you want to create a 3D scene including those extra details, and you manage to get the building converted/dumped into a voxel format, then it may be worth making models of all the furniture, trees, decorations, animals, hearthlings and so on that you want to use in the scene by using the model files from the game itself – that way, you can position all the “props” within your scene, and even animate it if you care to go that far!
I suspect that you’re hoping to do something more in the style of what you can do with Minecraft, where they have a “block for block” export function; but sadly Stonehearth doesn’t translate neatly into the same kind of export format since its building and terrain blocks are on a different scale to the furniture/items and hearthlings and animals. So there sadly is no “take a 3D screenshot/scan you can open up in another program” option; the closest you could get would be that old “dump building to model” method and then scaling it up to full size, adding the other models for things like furniture… and you’d probably have to create the building template such that it includes “terrain” (using terrain-coloured building blocks), since any of the natural terrain won’t be exported with the model either… so you’d have to include as much as possible into the building blueprint itself, and then when you have it open in your modelling program of choice you then add the details that are missing.
Whatever way you go, it’s a fairly involved process if you want to get full 3D renders; so it 's really worth considering what kind of rendering manipulations you want to do – if it’s possible to edit a still image to get the effects you want (e.g. neatening up edges, increasing contrast and adding lighting effects) then it may be possible to do that all in 2D/image editing and not have to worry about 3D models.