Why should Germany bother with the Med at all?
If we start this POD with no BoB then why would Germany need to distract itself in the Med? If Germany decides to "woo" Britain then it wouldn't be conducting the Blitz - in any form - and it would be saving itself up to "rid the world of those eeeevile Bolsheviks." The Mediterranean would be Italy's realm, not Germany's. Sure, make a show out of Sea Lion preparations and make sure the British know just how "lucky" they are that the Luftwaffe never got loosed to bomb flat every city in the entire UK. Propaganda, propaganda, propaganda. And in this OTL, there'd not be that certainty that England could "stand alone" as it hadn't had to. One "benefit" of the BoB was that the British realized that they were able to "take it" - as Churchill was fond of proclaiming. In this ATL, that's an unknown. And the German war machine is still unbeaten at this time and composed of nothing but ten foot tall inhuman killing machine soldiers with unbeatable Me-109s to back 'em up.
So if the Germans don't give the British any opportunity to learn otherwise it's to their advantage.
A Luftwaffe not ground up by the BoB would be in a better position to support the Italians in Greece. And any German troops deployed there would be a lot easier to then redirect east once Barbarossa started - this, as compared to troops and equipment sent off to help the Italians in Africa. No, this wouldn't much help the Nazi / Fascist alliance but what did Germany get out of that anyway? If Germany pretty much left the Italians to their own devices then the British would wind up directing most of their ire at the Italians rather than the Germans. It'd be the Italians that were killing British troops in Africa - not the Germans. Germany could further stir things up by quietly - and quite privately - get the word back to the "right people" in England that the Fuhrer really doesn't much care what Britain does to the Italians and won't come rushing to Mussolini's aid. Yes, it'd be yet another of Adolf's "solemn vows" but such poisonous words whispered in the right ears in England could play merry hell with any war plans Churchill came up with.
The overall intent of this being to portray Germany as being focused eastward, focused on being only a Continental power, not being an enemy of the British people, and only wanting peace between them. This, while at the same time subtlety reminding the British that it was only Germany's peaceful intent toward them which had spared them the defeat the French had earned.
With that as the propaganda message going out engaging in a Blitz or creating an Africa Korps would be counter productive.
And with such an otherwise free hand, or at least a "freer hand," Germany's Barbarossa could then enjoy an even greater initial success. That, in turn, would play right into the "let's not go an aggravate the Fuhrer" attitude being played up in England.
Once the Japanese step into the mess then this would only amplify. The Japanese would be attacking the British Empire directly. Germany's war with the British was only because of those "messy" Continental entanglements which those "stupid" politicians had gotten Britain into. Oh, and the French. Blame it all on the French.
The political chaos this could cause would be of enormous benefit to the Reich.
And really, what did the fighting against the UK actually gain Germany in OTL? Once chased off the Continent, what threat was England to Germany? No matter what it would be years before the British Army had reconstituted itself enough to even have considered a cross-channel invasion. What opportunity there was for Germany to have invaded England was one which disappeared entirely by the summer of 1940 and was unquestionably gone once Barbarossa started. So even the U-boat campaign wasn't necessary. it was just a waste of resources. It was never enough to bring England to the point of surrender as the UK was self-sufficient - if but barely - without any imports. Better then, to have used all that steel and manpower on the Eastern Front.
So this ATL presents the Reich the perfect opportunity for that.