I wouldn't say it's a problem with the registry so much as a, possible, mismatch between it and where the game is.

The install path for HoMM3 seems to be stored in HLM\SOFTWARE\Wow6432Node\New World Computing\Heroes of Might and Magic® III\1.0\AppPath. So for example if the game folder where moved the value there would no longer be accurate, however even if that's the case any half decent installer lets the user browse for the correct or alternate path.

Since Alex didn't give much info on troubleshooting, such as if he tried to set the path for HotA installer to the correct address to where his game is located (or even mention where his game is installed), so figured uninstalling/reinstalling, while avoiding using system folders, might be the simplest way to rule out an incorrect value in the registry and permissions related to system folders.

Does anyone know how to enable the debug menu?(window bar cheats) since the launcher directly interacts with the exe and the debug activates from a start parameter

It means it doesn't work with those builds of the game (1.0 through 2.2). It only works with Shadow of Death version 3.2 and Complete (4.0) that's sold on GOG.

You dont actually need the mod. I like the original experience. But here is the fix for all of it, whether its Heroes 3 or Chronicles games

Link
https://verokster.blogspot.com/2018/10/heroes-of-might-and-magic-i-iv-gl.html

Guide:

Step 1: Go to the root folder of Heroes of Might and Magic 3 folder. Copy and Paste "DDRAW.dll" there.


Step 2: In "Chronicles games" When you are in the root folder, click the name of the game folder that is already there. Then copy and paste it there


Step 3: Start the game


Step 4: Once the intro is over. Go to "Config" file and browse downwards til you see "Main Game Full Screen=1" change the value to "0". Then start the game


Step 5: Unhook "Aspect ratio" then click "Full screen". And there you go. Clear text (While the FMVs can be blurry) But its great that it works! The original experience without mods. So hope it works!

If you force 4:3 to 16:xx without aspect correction - you got blured image with - obviosuly - wrong proportions. So its not only for FMV.
For everything else - GL wrapper mod been a mod, but still provide most authentic gameplay experience, while HD+ mod shortly become been gameplay mod and not just widescreen\resolution wrapper. Something changed way more than just additional hex showing for enemy units movements (imbalanced already, and there is more).