Maybe not because of the poor performance - you know, not that simple - but because of the high costs and more importantly, more caution, not believing the war is - almost - over when France was about to collapse. As mentioned above, waiting, wait some more and some more.
For Italy, as a major merchant marine power, robbing both sides blind with "safe" transportation and breaching the blockade could be.. profitable. Exporting italian products mostly to Germany not only could create a hefty profit - again - but also could improve the industry to a great extent.
Of course, they would try to extort the hell out of everyone: territorrial concessions, trade deals, Suez usage preference, whatever, but IMHO there are so many possible outcomes, i see no way to predict the outcome (maybe Corsica, at least they try to go after Savoy, I dont think they get Tunesia and Malta is out of question. Dalmatia depends on what happens with Yugoslavia: in case of german invasion and breakup, they may simply occupy it, etc.)
Im conviced, that they more or less drop the whole greek war nonsense - they pressure the greeks for everything, but no war.
Japan would have a hard time, the men, material and everything used against Italy in this case go against them. Good time to extort... make a deal again with the brits.
Good question, what would happen to the minor axis: IMHO, they would flock to the non-beligerent neutral Italy to counterweight the german influence. Possibly Hungary remain non-beligerent with close ties to Italy, in case of Yugoslavian breakup, they would occupy parts in concert to "protect the inhabitants from the... whatever". Romania because of Bessarabia would most likely still go to war, Bulgaria would have followed Italy (and with the Yugoslavian occupation).
However, the whole Yugoslav question is flexible at least: in this case, the neutral Italy (and co.) are the biggest threat to her, not the germans. So maybe no coup, we could even see an axis Yugoslavia, Germany protecting her - from the Italians.
Germany overall would be better off: at least 2 theatres are off, manpower, material - imported or acquired trough Italy - situation is better, anything could happen.
However, after the US entry to war, things could go... interesting - and again, too many unknown factors.
If the war ends somewhat similar to OTL (bombing campaign, D-Day, Soviet steamroller, german defeat - oh, btw, maybe a Black Sea LL route is possible in this scenario), and Italy as above mentioned, in a "wait, wait, wait some more" mindset, they would declare war when Germany proper is under attack. Or even when Berlin is under siege. Hell, they may wait till Hitler is dead. The Alps are a bad palce to attack anyway, they dont really want any territory from them, why the rush.
Maybe, if Yugoslavia goes axis they attack, but only when the Allies at th egerman border - and near or in Italy.
After the war... hm, good question. First of all, Benny would seem as the statesman of the century (only a few would know, how close they were to go alongside with Adolf... shivering at the tought), still, US would pressure both Benny, the king and well, everyone, to "ease up" at least a little bit. A Franco-style power transfer is for sure, maybe sooner.
Without the war damage and with the, well, profiteering on Germany, the economy and industry would be in a much finer state than OTL. Hell, maybe they would set their agriculture straight during the war.
So... TLDR: they would be much, much more better off.