Without a doubt if the British move into Crete. Nothing the Germans opt for is really changing in terms of other theaters then. Crete might well end up being a smashing success with far fewer losses if the Brits don't go beyond Crete. The real question is does the British not going into Greece also mean not going into Crete? So if the British opt out of Crete in November 1940 then does Hitler not order Greece invaded? It think not personally.
I think that Germany is more likely to get involved in Greece if the British intervene - there are too many implications (Military and Political) of having the British establishing themselves in the Balkans.
As such an intervention cause the Italians to lose face I cannot see such an intervention happening if the British do not go to Greece.
This then would mean that - certainly in 1941 - there is no reason for the British to occupy Crete and subsequently no reason for the Germans to assault it.
Meanwhile the Battle for 'Greece' becomes very Static
Likely then all the Germans do is overrun Yugoslavia assuming that still happens in March (which it probably will even without British intervention into Crete). So Yugoslavia is taken down as per OTL and delays Barbarossa FAR less, while the Axis can then properly garrison Yugoslavia and Hitler can potentially force Mussolini into an armistice with the Greeks provided the Greeks agree to keep the British out and stay neutral or join the Axis.
I was under the understanding that the Balkans 'adventures' where not as much as a delay to Barbarossa as were the unexpected heavy rains that swamped the Forward Airfields in May and swelled rivers etc
I get the impression that the Greeks were having quite a good war vs the Italians - who had been bullying them for 2 Decades - right up to the point where the Germans and Bulgarians opened up a second front.
So until any intervention, its likely that the Greeks would fight on and Mussolini would lose too much face if he withdrew the Italian Army or agreed to any humiliating terms.
That opens up two different discussions then, what happens if the British move into Crete and what happens if they don't. If they do then Germany invades, but if they don't then perhaps Greece never is invaded by the Germans and the campaign peters out for the Italians and Hitler forces Mussolini to drop it after Yugoslavia falls.
If Germany intervenes despite no British deployment to Greece then I can see the British occupying Crete when the Greeks are defeated - if that still translates into a Parachute assault then I can see it failing as the British units sent to Crete would not be lacking Cohesion and reduced TO&E due to their defeat and rapid evacuation from Greece
So if no German Greek campaign and there is a ceasefire, Yugoslavia changes dramatically and so does Barbarossa. A neutral Greece is then an interesting wildcard in the Balkans, while Barbarossa can start on June 10th instead of the 22nd with two additional Panzer divisions (2nd and 5th aren't diverted by the Greek campaign) 300 more aircraft not lost in Greece/Crete, plus German paras. I wonder then if that is enough to get Moscow to fall. In that case strategically the Greek campaign for the British in 1941, despite the defeat, may have been a game changer in the long run and the right decision on Churchill's part. Libya then might also have been a strategic sinkhole for German resources that were more useful elsewhere, as if there is only a minor German commitment to keep Italian Libya from being overrun West of El Algheila there would have actually been a lot more resources for Barbarossa (an additional Panzer and motorized division in 1941 plus several thousand more trucks).
The failure to capture Moscow is not due to a lack of units/troops/tanks etc but a combination of Mission creep (as I understand it Moscow was not a primary objective at the start of the Campaign), Massive Logistical issues, poor terrain and General Winter - oh and the Red Army
And if the British are not fighting as hard or taking as many losses in North Africa then they would have more equipment to send to the Russians - as it was 1/5th of the 'Russian Tanks' defending Moscow that Winter where made by 'Communist Workers' in the British Midlands
53 of the 265 tanks from 7AD were refitted in Egypt and made an appearance in Brevity in May, which is a good indication of the state of the British after Compass: 3-4 months to refit 1/5 of the armour.
Without Lustre the only British armour between Feb and May would be the 2AD with ~100 light, ~100 cruiser and ~50 captured Italian tanks. IOTL without Benghazi the British couldn't supply half of these tanks, so getting Benghazi running is a must.
7th Armor Division formed a "Brigade group" using the runners it still had available - take in mind that a number of tanks had also been sent to Greece and likely sent to East Africa as well further weakening the numbers of tanks it had available in Egypt on the 24th March 1941
7th Armoured Brigade group - Op Brevity
A Company, 2nd battalion The Rifle Brigade
2nd Royal Tank Regiment (29 Cruiser tanks)
6th Australian Division Cavalry (~28 Light Tank Mk VIB)
7th Support Group (elements)
11th Hussars[4](Marmon-Herrington Armoured Cars)
One troop, 12th Anti-Tank Battery, 2/3rd Australian Anti-tank Regiment (2 Pounder Anti Tank guns)
22nd Guards Brigade Group also had 24 Matilda II of the 4th RTR
The Tiger Convoy arrived on the 12th May 41 - Brevity was launched on the 15th May 1941 so 3 days actually - not 3-4 months and elements of the Veteran units were still fighting to reduce bypassed Italian Garrisons right up to the 24th March so its not like they were sitting on their thumbs during this period!
Also I would seriously doubt that any of the Tiger Convoy tanks were involved as they would need to be unloaded, made serviceable etc and moved up to the front inside of 3 days!