In HOI3, without supply because Suez is closed Italians troops were rapidly doomed starving without supplies, unless they take Egypt and/or Suez. That was not perfectly historical.
In HOI4, as the "supply limit" system give you some supplies (equipments) for Victory points and provinces, we can think that Italian troops in East Africa will be able survive on their own with the (limited) local "supply limit" they have. That may allow more historical resistance from Italians.
In HOI3 (with HPP at least), puppeting Ethiopia allows Italy to draw on Ethiopian supplies - not enough for a huge army, but for a reasonable force. I think the HOI4 system makes more sense so long as it does not become too easy to "live off the land" when it's really not plausible.
True, and there are different rules to cover this. But, the Convention included Article I, guaranteeing passage to all ships during war and peace. However, this was in tension with Article X, which allowed Egypt to take measures for "the defence of Egypt and the maintenance of public order." The latter clause was used to defend the actions by the UK (as occupier of Egypt) in both the First and the Second World War and by Egypt against Israeli shipping after 1948.
Obviously, this applies only when UK is at war, not when Italy is at war against Ethiopia. Italy can send Army, Navy and supplies through the canal in 1936. But not once they invade France in May 1940, and then invade Egypt. Then the UK blocks them from using the canal.
Arguing international is usually a trap for fools when a war is under way, since powers (Britain being notably enterprising in this regard) do what they will and argue about it later. But as we are not yet in the game and at war, I'll go ahead anyway. Britain acted in a high-handed manner against both friends and neutrals during the war.Their motivation is understandable, historically and in game, but it does not make it legal. And if illegal, that creates the opening for diplomatic and military corrective action under the treaty.
Of course the British argued those provisions, but that tension does not create an inherent conflict if the belligerents conduct themselves in accordance with the treaty and no legal justification for violation of the treaty exists without specific hostile action proximate to the canal to justify it.
The rights and obligations of Egypt stand apart from the rights and obligations of the UK and other parties to the treaty, which are clear enough in the case of transit by a party without violation of the treaty terms or acts of war in the transit. As an occupier, the UK is bound as a party to its usual obligations and those of Egypt. Terms of free passage in arms but without engagement is an established element of warfare, often in the evacuation of cities or fortified positions or capitulations with honors of war or from an open city.
As a practical matter, the British piling up strong forces in Egypt don't need to violate the treaty to discourage its enemies from passing the canal in time of war or even approaching it since they are vulnerable when at sea, and make an effective invasion impossible. There are some procedural steps, but being the first to breach the treaty would put the UK in the wrong and justify diplomatic and even military action against it to restore passage, all beyond the right to station a few warships at the exit ports. It might be a welcome casus belli for direct military action against the UK to restore freedom of navigation and expelling Britain from Egypt is a credible objective to ensure that. I'm sure the Russians would offer to be responsible protectors of the canal.
I expect the treaty system is not sophisticated for the nuances, but the Dominions and allies of the UK, in the circumstances, would be justified in declining to engage in war in defense of the UK's illegal action.
Of course this requires some countries interested in pursuing corrective action - that would depend on the flow of the game. If the war played out along historical lines, I don't see countries other than Italy with motivation to challenge bad faith closure by the British, but the world can take other paths and a casus belli for a limited "police action" type of war could be quite convenient. Would be a shame to destroy the canal in the fighting to free it.