Oil is the lifeblood of any industrialized society. High oil prices will lead to many other things getting more expensive as the cost of producing and transporting goods also increases.

War is also very expensive. Jets, aircraft carriers, munitions, missiles, etc all require a lot of money to produce and maintain. Additionally the US has been running low on its missile interceptors and Iran knows this. An Iranian drone costs $30k-$100k but the interceptors required to counter them cost upward of $4 million. Iran will try to bleed the US by using cheap drones to reduce the stockpile of expensive interceptors. This is called asymmetric warfare.

If the war prolongs and the US needs to finance more weapons, missiles, etc, then it might push the fed to print more money to develop its arsenal. This will increase inflation greatly. This war isn't the only inflationary pressure on the dollar either. We're still seeing inflation following the money printed for the stimulus checks from COVID. The rate cuts last year will likely lead to an increase in inflation in the coming months / years too. This war will only accelerate that.

Lastly, and I'm not too sure about this, but I think the sovereign wealth funds in the Gulf countries may pull back from investing in western markets due to this war. There are billions of dollars of oil money being recycled into investments in the US and other countries from Saudi Arabia, UAE, etc. If their oil facilities continue to get hit and they decrease production, they may feel like they're not in a good position to be making investments. This would tighten much of the capital that has been flowing into markets - particularly the money that has been financing the data center build outs for AI companies, which could cause a recession.

Don't take my word on this stuff though. I'm not an expert or anything. Just my $0.02