Let's look at this in three ways as I think the changes are very big.
First British logistics get a whole lot easier as others have stated. They can use Suez and have a good choke point at Gibraltar to aggressive patrol and restrict U-boat penetration. Assuming no French North Africa campaign, the German u-boats cannot reliably use Toulon as a base, so they have to leave St. Nazaire, go through Gibraltar, do their monkey business in the Med and then come back through Gibraltar and back to the Bay of Biscay. They don't have the range to stay for long. Escorts might be needed in the Med, but they can be fairly short range, low performance ships.
Germans never figured out how to get past the anti sub defense at Gibraltar on their own. The Italians showed them how to use the deep water currents to coast quietly past the defenses. To get subs into the Med they'l have to bring them down the European canals.
The Brits will need to keep a corps or two supplied in Egypt, but again, logistics are easier as they can go straight through instead of around the cape in fast/high value merchant ships. That Egypt force will also not be using tremendous amounts of consumables nor sucking up the cream of the Imperial armies in terms of talent. Makes LL a bit of a delay as the Brits were spending the last of their hard currency on equipping their North African forces. Won't be much of a delay ( a few months) but a delay none the less.
Furthermore, the Royal Navy will not be engaged in the Verdun of the Meditarranean. They don't have to supply Malta, they don't have to interdict supplies from Italy to Libya, that don't have to defend Greece etc. IIRC, the RN lost a third of their pre-war cruiser force in the Med. Ships won't be sunk, ships won't be damaged. That means either more ships are available at any one time, or preventive maintenance can be performed on more ships with routine refits/dock periods.
Savings for the British are immense. Only down side is it allows Churchill to bother his marshals more often about the blue arrows he liked to draw on the maps. Who knows where that might lead?
Now what does this mean for the Far East?
The Royal Navy can actually support a modified Main Fleet East movement in the summer of 1941. They have a major commitment to Home Waters to contain the German surface fleet and run convoys to the USSR, but no other major capital ship committments. A few ships will be kept in the Med to watch the Italians, but the R's and non-modernized Queens could be sufficient as a deterrent. Sending a couple of carriers (say Invincible, Formidable and Ark Royal) plus a three or four battleships/battlecruisers and two or three submarine squadrons to the Far East as well as having the Australians and New Zealanders send a full corps to Malaya during the first half of 1941 changes the Pacific war immensely. And since the RN and RAF is not seeing massive losses in North Africa, there should be more modern aircraft with better pilots, better staffs and better equipment available for Far East committments.
Best case is avoids a Pacific war entirely. Next best is the Japanese effort to capture the DEI is thwarted in the spring of 1942. Even if the defense of Malaya is somehow bungled the stronger Brit defense there will attrition away Japans offensive air strength months earlier, with the Japanese losing their ability to make stratigic offensives by May or June vs October or December.
Now let's look at the Germans. The biggest thing is not the formations committed to Africa and the Med. An extra Panzer Corps somewhere will help the initial stages of Barbarossa. The big thing is the logistics. IIRC the Afrika Korps divisions were logistically 10x as expensive to support as a division in Russia. The desert played hell on equipment, mechanized forces were a requirement to fight there, and quite a bit of the supplies intended for the AK were sunk on every run into Libya. Freeing up thousands of trucks and thousands of barrels of gasoline burned every day in Africa probably has a bigger effect in Russia than anything else.
Very true, although it cant be calculated with a x10 increase in logistics support for the eastern front. Primarly factor is the Italians carried the majority of the logistics burden there; providing automotive transport, their short railway, and coastal freighters, plus manpower. Part of that could be made available from a nuetral Italy, but at a cost to the Germans. Plus a lot of the resources would not be practical to provide.
A second smaller factor is the Axis were seldom able to provide a sustained daily requirement per battalion. Medical supplies, rations, spare parts for vehicles and aircraft, ect... and most important artillery ammo averaged well below both the book allocations and actual battlefield needs.
Bottom line is the increase in the east from a lack of a African campaign is not at a 1-1 ratio to expendenture in Africa.