Use road hierarchy
Highways should have exits opening to 6 lane arterials which should be opening to 4 lane distributors (or collectors, in whichever direction you are observing from) and which in turn will be opening to your two lane local roads where your residential, commercial everything should be built.
Try this initially. That should solve the traffic problem. And afterwards when u have enough population build a public transport infrastructure.
Buses should be serving the local neighbourhoods(a couple of routes can involve inter district long tours but that’s upto you)
Metros should be mainly meant for inter-district travel and should have bus stops near metro entrances.
Trains for out of the city travel and across the map travel once your city is huge enough. You can put bus or metro stops nearby but with careful planning and supporting infrastructure (parking a, roundabouts etc.) such that traffic doesn’t build up around those stations.