Every time this question is asked, a ton of people recommend the Spyderco Military, Police 4, or similar Spyderco folder. While Spyderco's folders might cut better than the average modern folding knife and can offer fantastic edge holding, they have significantly thicker edges and blade stock and do not come close in cutting performance to a basic Opinel. I can't fault people for recommending Spyderco, but they really don't make much that comes close to what OP is asking for.
I'd also add that the TRM line of knives aren't incredible in this regard either. While they use .080" thick stock, they still grind their knives to be quite thick at the edge. I believe my Atom was about .025" at the edge with a factory grind; for comparison, I have an Opinel #8 here that is sharpened to 15 dps and it's still about .005" thick at the edge, 5 times thinner than my Atom was. You absolutely feel that difference in use.
Unfortunately there is not a plethora of modern folders nowadays that offer thin blades and, crucially, thin edges, but the Manly Peak seems to fit most of your requirements better than what I'm seeing recommended here. They're available in D2, CPM-154, or S90V for quite a reasonable price, and they're ground to cut things. The model with a spyderco-like opening hole uses .120" stock, which isn't terribly thin, but the edge is like .008" thick sharpened to 15 dps and the tip is very thin. They also have a model called the Wasp which is a smaller slipjoint model with a similarly thin grind.
Upon seeing your request, it reminded me that the Peak has been tempting me, so I went and placed an order for one.