I partially solved the problem by binding equipment to the army window. Now it only shows on the hero, enemy hero, castle, caravan, and garrison (but I haven't checked that one).
So I generally have an idea of what should happen, but I don't know how to do it properly.
I envision it roughly like this: you'd need to bind a link to the window (that opens when you right-click a hero) to additionally open a hero window (configure the connection), specifically the inventory section. At the same time, duplicate the new window (hero-inventory) separately without touching the original, and edit it so it doesn't open full-screen, but rather a specific area (the place where artifacts are displayed).
Added after 31 minutes
Unfortunately, simply adding references to icons from the inventory won't implement your idea. The game uses UI/HeroScreen3/Single/Icon.(WindowSimple) and substitutes artifact icons based on the Slot_1 and Pic variables. Unfortunately, defining new variables without modifying the exe is not possible. In particular, implementing your idea requires setting up the necessary functionality at the adventure map level in code. I think the Heroes V Universe development team is quite capable of doing this if they find the idea interesting.
That is, not trying to display icons from artifact slots in the inventory.
But instead displaying a piece of the window from the "hero-inventory" section, cropped exclusively to the inventory area — I don't know the exact size of the inventory where equipped artifacts are shown, maybe 500x500 pixels.
This way, the developers have already taught the game to display info about equipped artifacts in the hero-inventory window, and we just teach it to display a piece of that "windows-screen/hero-inventory" elsewhere as well.