I have to disagree, just imagine the efforts spent on Stalingrad rerouted to supply Africa Korps, which in this TL might well become an Africa Armee. Also imo certainly Malta WILL fall in 1942, doesn't matter how many troops the germans and italians will lose taking it, it will be only a pinprick compared to the forces available, and that will remove a large part of the losses caused to the german and italian ressuply effort. In the air, Luftwaffe redeployment would easily assure parity in numbers, and given the still superior german aircraft at this time to what the US and UK have, things will go badly in the air for them.
As to ME, let's not forget that US and UK still have a finite quantity of troops and materials, with an effort focused in North Africa, THEY will be pressed to find the troops and gear to mount a defence of ME, while it may be true that losing ME might not be catastrophic for them, it will give the germans access to yet more oil, and probably they will actually take the Suez canal as well. The germans might face problems supplying their forces, but certainly they'll manage to keep at least part of their available forces supplied, surely with all the resources and slave manpower available they'll try to build and extend roads and railways, use everything available in the Black Sea to supply their troops, air transport etc.
There was Panzer Army Afrika in January 1942 OTL, later redisignated German-Italian Panzer Army and Army Group Afrika. OTL the Stalingrad effort got on its best day 262 tons of supplies (Average was 85 tons a day), the Axis in Afrika was getting 1500 tons a day through Tobruk alone
Road and rail building takes time, lots of time, especially in rough terrain, like the Caucuses. This is a matter of many months, if not years to build up the logistics in the Caucuses to support overwhelming force, by which point there are enough WAllied forces
With more and better raw materials, not only the Me-262 will have better engines, and get to be built in huge quantities well before any of the US/UK designs even reach the frontline in numbers (Meteor F3 was inferior anyway and i don't think the P-80A would be terribly good either, and anyway, like mentioned above, they will only start counting in an invasion because of their short range), but also instead of the OTL Jagernotprogram, they might go straight to an advanced swept wing fighter like the Ta-183 and similar designs (because they would be not under the OTL great pressure for something, anything cheap and simple to put in the air which resulted in the He-162) so by the time the Meteor and P-80 and Vampire appear in numbers, they will have to face THESE, sort-of a MiG-15 but 2 years early. The P-80 and Meteor didn't do well against the MiG-15 in Korea.
PS: The americans will very likely bring the B-29 in Europe to attack targets deep in the east, but the thing is, because of it's higher speeds it's paradoxically a better target for the new jets, again this was proven in Korea. Would actually make the Me-163 more useful that it was OTL, against the faster and higher flying B-29, especially when also fitted with R4M rockets.
262 would have better engines, but that's mainly a logistics saver. It maybe has a 3 month advantage over the Meteor. OTL Allied jets were reserved for home defense due to their thirst and lack of need, if needed they could be deployed to the front to maintain air superiority
The Ta-183 essentially did get built OTL, by Argentina. It took 10 years to go from first flight to Service, Germans might do better, but they still will take time. More advanced jets take time to debug. The Vampire flew in early 43, no German jet fighter besides the ME 262, the HE-280 (inferior to the 262 and cancelled), HE-162 (flew in Jan '44, emergency design, good despite that but not easy to fly and lightly armed, plus had issues) and the Go-229 (only as Glider, summer of '44, likely to prove problematic in service due to issues with flying wings) actually flew, Vampire is almost certain to beat any super high performance jet into service
What made the Mig-15 so nasty was the engine, which was a British design. Note that despite capturing plenty of different German engines the USSR chose to copy a British engine instead, the Nene which entered production October '44