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I'm sure that such a version of Heroes III doesn't exist, because for this, the game would have to be almost completely remade.
The difference in graphics from the Doom II you mentioned is as follows:
Doom II contains wall textures, after which, at any resolution, it performs its transformation according to the principles of constructing a three-dimensional image.
In Heroes, the situation is fundamentally different. If you unzip the \data\h3bitmap.lod file (there is a topic about this on this forum), you will see that all the images displayed in the game (from background images with buttons to player flags, images of buildings in castles, etc.) are all ordinary bmp files that are displayed by the program without distortion.
Even if we assume that there is a file that contains the coordinates of the displayed objects, the formulas for transforming from the cell number to the window coordinates, etc., then to meaningfully change the resolution, you would have to redraw all the graphics, and in my opinion, this is more difficult than rewriting all the other components of the game.