My thinking is that through Gibralter, the Germans can launch an invasion of NA and into the middle east, to cripple Britain's oil supplies. Taking Gibralter cuts off allied shipping in Mediterranean so supplies can be shipped to the German army in the middle east. The shipment of raw goods from the Soviet Union ended in August of 1941 and this Mediterranean offensive would begin even earlier than operation Barbarossa because there would not be a need to wait until spring, perhaps the agreement is extended as the Soviets would have been more than happy to wait until the Germans are weak to strike. Once the Germans break through the Suez they will face little resistance from French Syria and the British mandates, they were very underdefended and on top of all that the Arab nationalists would rise up and help the Nazis overthrow the British and French. From this position, they can invade the Soviet Union from Poland and the Caucuses.
The USSR surrenders (not unconditionally) because the war on the eastern front would inevitably end in a stalemate, seeing as the Soviets are the aggressors they would be more willing to make a deal with the Germans. Perhaps Stalin and Hitler die before war's end and the new governments decide to make peace with each other rather than sacrifice more and more lives. And the US would drop out of the war in Europe as soon as the Soviets did, leaving only Britain left. I will concede that realistically they would surrender at this point but I at least wanted to consider them to still fight on.
If the Axis could not reach Alex from a starting position in Libya - how does holding Gib change things?
Once the Germans Break through the Suez? We would still be waiting today for that to happen. The Majority of the Allied supplies in Africa either went across the continent or around it once Italy entered the war. The Tiger Convoy is the only convoy that I can see being impacted here ands it now goes the long way around
Malta won't fall right away (if it does fall) that might take a year or so from Jan-March 41 which is when I think the earliest moment that Felix can be launched - unless Germany drop whatever FJs they have not long afterwards - in which case, successful or not they wont be able to take crete as the FJs will have been ruined and not fit for purpose.
The DAK arrives in Libya effectively beginning 41, they would have to achieve all of this taking Egypt and conquering half of the Middle east before mid 42 as that is when the Allied war machine has gathered enough steam to start overcoming the shortfalls that impacted the Allied forces in 1940 and 1941.
I know they were good...but not that good eh?
And Britain 'surrenders' when the Swastika flies over Whitehall and jackboot march down the Mall. Losing Gib in 41 does not allow that to happen.
So ultimately the Axis gain the basket case that is Spain as a net drain Ally (think Italy but worse) - Im sure that Blue division will come in useful somewhere - certainly the remnants fought well in Berlin - cut off the Western End of the Med and possibly reduce Malta by the end of 41
They however lose the North Atlantic Islands, whether or not the Axis preemptively reinforce/stage forces on them - the Axis cannot maintain a base in the Atlantic anymore than Britain could maintain a base in the Baltic and the British will do what they must. Salazar might rage away in public but he was a smart cookie - he would understand. This has implications for the BoA and possibly has it being won by the allies before May 43. An in this scenario maybe Torch and Husky do not take place where they did and Normandy comes early?
With Felix I doubt very much that the British would send a corps to Greece and would instead not lose a Division worth of men and 5 divisions worth of equipment between Sonnenbaum, Greece and Crete.
Crete is held by the Allies as instead of knackered units with incomplete ToE being dumped on the place after being evacuated following the fall of Greece - fresh units garrison the place and the FJs cannot answer the phone at the moment as they are busy filling wargraves on Malta or Hospitals in Italy (and possibly POW camps elsewhere if Little Hercules went south).
Sonnenbaum or its equivalent here - has a steeper cliff to climb - as the best Allied units are not skimmed off to fight in Greece they are instead sitting in Egypt!
This also means that further forces can beat the snot out of any pro axis Arab uprising even more than they managed OTL.
Another thing to consider here - Franco might have been mates with the Fascist leaders but many of his Spanish peers in Government were also good mates with the British! And all knew, unlike Benito, that the only winning move is not to play.