It looks like Corona used to have extensive mining (the illicit mine behind the Snuggly Duckling and now the tunnels under Varian's village) but it all the decorations in the palace are all sun and sea. Yet the forest is only lightly touched, you would think wood get scarce after few centuries for building material and fuel, so they are rich enough to pay to leave the trees alone. But Corona seems so small, the wall looks to be ~10 miles from the palace. I wonder how they do it.
What makes you assume the mines connected to the Snuggly Duckling and Varian’s are illicit and not just abandoned?
As for the forest, let’s go to the map, shall we?
If you look off to the bottom left, the map calls the woods “Big Forest”
It’s difficult to say how far the forest goes. We’ve seen so little of it, really. And no one says that wood cutters don’t go farther into, let’s call, “unincorporated Corona”, beyond the wall to get their wood, leaving part of it to be scenic for view from the palace.
But yes, Corona appears to be very wealthy. I personally headcanon that they have an active vineyard and winery, as is evidenced by the wine in Tangled Ever After.
As you can see, each and every one of these barrels is stamped with the mark of the Snuggly Duckling, which means the pub itself is also associated with a winery. Also
they keep barrels in that abandoned mining tunnel previously mentioned.
A really good wine industry could easily make Corona a wealthy kingdom.