I would have it fully and professionally restored. Currently it’s only value is derived from the fact that it’s a Navy Luger. That’s cool and has value, but it’s in absolutely horrid shape. A poor entry level collectible for its class. It would appeal to a shooter that wants a “cheap” Navy Luger, but few others would consider it highly.
Now if you restore it, it will lose its originality. However, how much value is that collectible originality contributing in this shape? I would argue that originality contributes next to nothing in its current state. Now if you restore it, you’ll wipe that collectible value away, but you’ll massively increase the shooters value. I don’t know what a Navy Luger goes for, but I bet a shooter, or even a less-well-off collector would pay 50-70% of the equivalent “collectors” piece for a gun in beautiful shape, and I suspect that amount is still 100-200% more than what’s it currently worth in its sorry state. That’s my guessing. Maybe someone with better knowledge of the Restricted Luger market will chime in.