The court concluded that the POTUS has presumptive immunity from criminal prosecution for all official acts--those that fall within in the outer perimeter of his duties-- or acts is that are "not manifestly or palpably beyond [his] authority."
The court goes on to say that if the government wants to prosecute the POTUS for a crime, they have the burden of proving that the prosecution would "pose no dangers of intrusion on the authority and functions of the Executive Branch.” Such a ruling seriously hamstrings any effort to hold a criminal POTUS accountable since much of the evidence for criminal conduct is going to involve interactions with government officials.
It is just wrong to say that this ruling does not immunize the POTUS from criminal acts, that is exactly what it does. As it stands now, the president can order parts of the executive branch to engage in criminal behavior, like murdering political rivals or seizing voting machines, and he would be immune from prosecution because his actions (giving an order to executive officers) are "not manifestly or palpably beyond [his] authority." All he would need to do, as the law stands now, is come up with some argument about how his prosecution for a crime interferes with executive function. An extremely low bar.
Also, this is new law. Most of the cites you give deal with civil immunity, not criminal immunity, this law immunizes the POTUS from crimes.
I went to one for a candidate for the House district I lived in a few election cycles ago, It was mostly stump speeches and other "rah rah we're gonna win!" style pontificating. But one thing I did not expect and I actually found interesting was the house candidate spent a lot of time introducing other local politicians that were in down ballot races in the district. City council seats, education board seats etc. That turned out to be really useful, because it meant I got to meet/ hear from candidates who I either had no idea existed or who were just a name of a flyer before then. I suppose that experience may not transfer to a national candidate rally though.