EDIT 15 hours later: Yamagami claimed to have a grudge against an unspecified 'religious group' to which he claimed that Abe was associated. Would be hilarious if he was referring to Jews.

It's just wishful thinking: that someone, somewhere just sent a message to the enemy by taking out one of their top men in Japan, setting off a sort of 'spark'.

Japan is Left-liberal enough that Abe probably is seen as too conservative/nationalist by the average Jap. There simply aren't enough Japs who view him as too Left or liberal, those who would see him as a 'cuckservative' or whatever, for it to be statistically likely. On the other hand, the number of people anywhere Leftward of himself, those who view him as a 'fascist', would massively outnumber the former. He'd have the whole Left gunning for him from one side, people who are probably ecstatic right now, as opposed to only a small number of genuinely Far-Right people from the other.

I'm sure we'll learn it'll be about late modern problems and processes such as social atomism/disintegration, identity crises and recognition. About feeling alien, excluded, homeless, marginalized, out of place, unsynchronized; as someone who is only Japanese in superficial ways (e.g. by citizenship) and not in any authentic way. About being the 'outsider within' and 'together alone'. About feeling a need for some kind of emancipation, liberation, a need for revenge. Yamagami is unemployed, and we don't know why he left the SDF. For all we know, it was perhaps because of bullying over non-Japaneseness. He probably read all of this into Abe and felt that killing him would be an emancipatory, liberatory, symbolic act that would put him at ease, releasing all that pent-up hate, fulfilling life's purpose, possibly even making him a martyr of sorts. He probably planned it for a long time, without knowing exactly who to lash out at. Upon hearing about Abe—somebody who personifies 'capitalism' and even 'fascism' as defined from a broad Far-Left viewpoint—campaigning somewhere near him, he probably spontaneously decided to act then and there. That's probably why he handed himself in immediately thereafter; precisely so that he'd get the death penalty, in the hope that he would be remembered by the 'oppressed' for his actions everywhere.

It won't be a Far-Right motive, such as restoring glory or honour by taking out a shameful puppet and/or traitor who symbolizes inane consumerism; 'cuckservative' politics that shut out actual Right-wingers and do little if anything at all to slow down, let alone reverse, Leftism or anything else; multilateralism/globalization rather than Japan First; and so forth.

I think it's also possible that Yamagami hated Abe because of Covid or the Covax, since he has been since reported (unconfirmed) as claiming he had no "grudge against the former Prime Minister's political beliefs". If he lost a relative either to Covid or the Covax—and Abe was indeed in power during the beginning of Covid—that could also be a non-ideological reason for being opposed to him.