Oil output wont increase, bcos oil went so low before the war that their budget ended up running into deficit. This is their chance to make more money before war subsides and electric vehicles take over gradually in future.
Add to that US pissed off saudi strong man MBS and dissed UAE on F35 negotiations. So both these countries have an axe to grind against US. Next is US negotiating with Iran for nukes & increased oil supply, this is making the rival saudi camp uncomfortable. So all in all US has managed to burn every bridge & boat.