السلام عليكم ورحمة الله وبركاته Ustadh, we know it is allowed to raise the hands when the imam makes dua for rain in the Jumuʿah khutbah. Can we make qiyaas from this and say it is also allowed to raise the hands when the imam makes other dua’s in the khutbah?

That is not how we do qiyas, in a matter of fact every single thing was reported, so if they raised their hands this would have been reported too, but every single thing was reported except for this. We can't make qiyas on something that the Prophet and the companions abandoned even though there was a need/cause for it, quit the opposite it becomes a sunnah to abandon it.