@ExNihilo
Well Germany is pretty well off in this scenario tbqh. Oil production in Germany peaked in 1940, the exploitation of the Austrian oil fields just started and peaked in 1940 IOTL.
Germany basically has dibs on any Romanian oil and no one who could seriously threaten that. I don't see who would start a conflict there.
Axis tanks, planes and ships could function just like IOTL. So there isn't an abundance of oil but enough to keep going for the near future. Especially with further investments in synthetic fuel production.
Labor: What stops Germany from "acquiring" all the labor they need from occupied (or unoccupied for that matter) European nations. France, Belgium, Netherlands, Poland etc. Its doubtful that they would require much forced labour, ITTL Hitler could and would probably demobilize a significant part of the Wehrmacht.
Britain's situation is much darker than you see it imho. Getting a substantial oil production going in Texas takes times and a substantial build up of infrastructure. Both things that Britain couldn't afford.
And we haven't talked about food security or how such a ressource starved GB is supposed to win against German submarines....
GB would imho sue for peace fairly quick.
Some of my ideas:
I don't think that Great Britain could continue the war very long. The sudden collapse of the world market and the complete absence of support from the Commonwealth would quickly cause starvation. Reduced production capabilities and a really unfavorable geopolitical situation would quickly render them a second rate power, heavily dependent on imports from continental Europe.
I don't think there would be serious attempts to conduct Sea Lion, the Third Reich would probably slowly extract political and economic concessions by threatening to withhold food imports.
Britain is probably going to experience a slow slide into Fascism. The government would be forced to comply more and more with Nazi demands, outlawing the labour party, releasing Fascists from prison, close cooperation with German intelligence services and stuff like that.
Britain would be one of the best places to live in Europe but would slowly assimilate into the "New European Order".
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Italy is another interesting case.
Their status as allied nation and the birthplace of Fascism might give them some leeway for a while. Their weakness relative to Germany and their rival brand of Fascism might make them a tempting target for a German intervention/invasion though.
Italian "not-as-racist" (at least compared to Nazism) Fascism has the potential to be an ideological counterweight to Nazism.
The absolutely fucked political spectrum in Europe would probably be:
Paternal Autocrats----Fascism-----NatSoc
For Italy it all depends on how well they can defend their independence. They could get their desired "New Roman Empire" or they could quickly become a satellite state of Germany.