If Italy doesn't enter the war, do the Germans bother with North Africa? Sure, they hoped to take the Suez Canal, but if they don't bother with North Africa, they only need to protect the coast of Greece (presuming they still take Greece, but a lot of the involvement in Greece was to my understanding them going to rescue the Italians from their Albanian adventure.
The whole reason why Germany got involved in North Africa was because of Italy's screw up. And the whole reason why Germany got involved in Greece was also Italy's screw up. If Italy hadn't invaded Egypt, she would have most likely still invaded Greece, as Mussolini had ambitions on sort of restoring the Roman Empire, forming an Alliance of Latin countries, conquering "living space", expanding Italy's African colonies and making Italy the dominant power in the Mediterranean.
Italy's invasion of Greece would probably still end poorly, but now the question is whether or not Germany or Britain would intervene? Since Italy isn't at war with the Allies
and she isn't an ally of Germany, they'd little reason to. Italy might try to to get Bulgaria to join in against Greece.
If Italy conquers Greece, Yugoslavia would be next and she would be pressured into joining Italy's sphere, which may cause a coup or a civil war.
Germany's main goal was the conquest of the Soviet Union. If Italy was waging wars in the Balkans or the Mediterranean, I don't think they'd care as long as Britain wasn't involved. And that all of this didn't harm Germany's attempt to ally with Hungary and Romania, who she'd need for the coming invasion with the Soviet Union. The same would be true if Italy doesn't Invade Greece at all.
If Italy doesn't defeat Greece then it would be an embarrassment for Mussolini, but I don't think it would be enough to get him deposed yet.
In any case, without North Africa and Yugoslavia to manage, Germany would be able focus more on the Eastern Front and have a few more men to spare, but I don't know it that would change much.
But the most important thing is: Without a weak target like Italy though which they could bring the fight to their enemy, Britain would have nothing to do. If Britain decides to hold on, and is supported by the United States, then Germany would still declare war on the US. The Torch Landings would still happen, but instead of proceeding to Sicily, they would land in Southern France next.
Goddamn. There's so much to consider that I don't know how to format it all neatly. And it starts to hurt my brain. I hope this is shitty enough for this shitty alternate history thread.