The sentiment in the news sources above, which try to pass Abe as a right-wing Trump counterpart, are way way off.
Japan is generally a conservative country when it comes to social order. Abe was considered one of the most progressive prime ministers in a long time, committed to pulling Japan towards globalization, which is sold as one potential solution to Japan's concerns about staying relevant in the modern world.
Abe was pro-trump because trump was anti-china. That's it; it's that simple. Japan relies on US for its security guarantee and instability in the US and pro-china sentiment makes them very nervous. That's easy and as far as tge Trump link goes.
Abe was generally progressive and globalist. He opened up to cheaper rice imports from abroad. He opened up tourism, especially for the rest of Asia. When I went to Kyoto in about 2019, the usual serene tourist spots were swarming with Chinese and Korean tourists wearing fake kimonos and taking selfies in rude spots. He also loosened immigration, or at least what's considered loosening in Japan.
Right now visas are still shut down with Covid as the excuse and I think they like it that way.
If this guy that shot him was politically motivated, it's probably more likely to be someone who disagrees with his globalists policies. I.e. someone more right wing. Not somebody who assassinated him for being too right wing.