It is merely a part of a value chain. Namely, minerals and petrochemicals have to be produced upstream. Financial GDP captures the ability to produce or purchase the upstream resources, manufacturing alone does not.
Now manufacturing capacity is illiquid, and it takes time to convert financial power to manufacturing capacity, see the Ukraine ammunition crisis. While manufacturing capacity is more war-ready.
However, China hasn't invaded Ukraine yet, because US choking off the sea lanes will be catastrophic for China's economy and offensive war capacity. Without trade, the factories have no resource inputs, and no markets to export to.
So in the end, financial power does slightly underestimate the hard-power benefits of manufacturing, but GDP (USD) should still be used as the primary determinant of hard power, not amount of factories built.
Sure, manufacturing depends on its inputs. My take is that the material economy (manufacturing and all its inputs) is the actual source of hard power, finance is a proxy, and maybe not the most helpful one in a case where war materials are controlled by an opponent.
That's too reductive.
1. That ignores established stores. One of the enormous advantages that Russia has over Ukraine is its enormous store of tanks, artillery pieces, and armored vehicles. Not all of them are state of the art, but they're a lot more effective than a rifle.
2. That ignores the pace of innovation during long wars. Just look at the pace of innovation during WWII. Or even later wars. New designs for rifles, tanks, planes, etc. come out quickly when people start dying en masse. Existing manufacturing lines may not be very relevant if they can't be modified to support new equipment types.
In a sense, you have to go 1-2 steps back to "the machine that builds the machine". How quickly can tooling be brought on line. How innovative and productive of a workforce do you have? Those things are related to manufacturing capacity, but are not the same thing.
3. Access to raw materials. One of the major reasons Russia is able to maintain its war against Ukraine is because it is a net exporter of petroleum products. If they were a net importer instead, global sanctions would be able to make them effectively stop within a few months. Petroleum, steel, food, etc. are all necessary commodities. If any of them can be embargoed, that is a massive weakness that is hard to compensate for with manufacturing.
There are probably other factors, but those are the main ones I could think of off the top of my head.
I like your "machine that builds the machine", I think that's actually the point I was driving at in the original post. Finance can accomplish much, but, at least during war, it is not a substitute for the physical economy.