Your big arterial roads have too many intersections that slows down traffic on them. Ideally vehicles should be able to drive fast with minimal stops on them. Because you have so many intersections it's slowing down traffic on the arterials which then is backed up on the feeder roads connecting to it.

My advice would be to halve the amount of connections between your smaller and bigger roads as well as adding public transit that isn't buses as that will ease up on the amount of non commercial vehicles. I'd recommend metros if possible or even a monorail if you want to connect just a few distant dense parts of your city as that will remove a lot of the normal traffic from your road entirely. Adding the encouraging biking policy can also help and if you have some empty green space next to a big road put a bike path alongside it and that can also help ease congestion. I also didn't get a good look at your zoning but I've found that not zoning next to your larger roads also helps as that's less vehicles stopping there. Hope this was helpful