And also Gondor had to deploy 2/3 of its forces in the south, where the most populated areas were, and Aragorn brought some of them on the ships, captured from pirates.

That would fit. Harad send iirc 10000 men to Sauron's army but all them were riding under one banner so they were probably from just one polity there and the rest of Harad might want to get some sweet revenge on Gondor for centuries of colonialism if they seemed to be weak.

TBH, if Sauron guarded Orodruin, he would have won. He had amassed a decisive material advantage by that point, and the only thing he didn’t have was time to apply it.

Yes, but he DID guard the Orodruin, that massive army did not stationed in Black Gate for nothing, he just did expected military invasion instead of two hobbits, and to be fair hobbits did seem to have some natural protection from his magic which was mentioned by Gandalf iirc. Also the Black Gate army was literally everything he had left at the point, and those probably weren't his best soldiers, those went with Witch King army. Other thing was that Western armies had absolutely no coordination or war plan at all, except Fellowship mission everything was improvised on spot.