The mesh looks like it was produced using the marching cubes algorithm (without vertex position interpolation, causing this specific look). In marching cubes you sample a field of scalar values using a cube-like construct and then repeat that process for all the coordinates, effectively marching the cube through the scalar field - hence the name. Based on what parts of the cube are “within the model”, you then use a lookup table to decide on the vertices to place there. Effectively you are polygonizing a scalar field here, similar to how MRI scans do it (which is where the algorithm originates btw).
The scalar field in game development mostly comes from combining coherent noise functions, like perlin.
To then later edit the terrain, you would need to edit the scalar field and redraw the terrain / chunk.
Be aware that mesh generation and alteration is a rather adcanved and complex topic, especially once you consider performance. If you want or need to implement marching cubes, the algorithm is described pretty well here: http://paulbourke.net/geometry/polygonise/
Sebastian Lague also has a good overview video on it with nice visualizations.
If you only want a sheet-like surface (no caves or overhangs) like in your screenshot, then it’s a lot easier to draw and manipulate the heights of individual vertices of a flat plane. You could still sample a coherent noise function to get the base terrain shape and still create an editor allowing you to create mountains or holes - just no caves or overhangs.
You will find a lot of good videos for starting out on this approach when searching for procedural terrain generation in Unity. Brackeys made a couple videos on it, and Sebastian Lague has an entire series on it as well.
You would, however, need to fake the specific look shown in the screenshot.
Also, while not increadibly hard after you got the base working, you still need to create your own tools for editing the terrain. For most things like creating mountains or holes this is rather easy to achieve (since you’d just increase or decrease the scalar values in, for example, a sphere shape over the mesh, and then redraw the chunk), but other edits may be more complicated, depending on what you need. I dont think so, but if you plan something like 3D sculpting, where precision and detail is very important, you will have to look into more complicated algorithms like dual contouring.
Dont if you dont have to tho. Dual contouring is basically marching cubes in way more complicated.
This is a rather broad comment, since i wasnt sure what exactly your goal is. If you need further information on any of these topics just let me know. Hope this helps for now