Only if there's a corresponding drop in the number of cars in use. It could be that people keep their old, inefficient, polluting cars for on the road for longer rather than replacing it. That would be bad for the environment.

There is some disagreement about whether this is actually the case. It takes a lot of resources to build a new car. Meanwhile the average passenger cars has been above 30MPG for 15 years now and the newer ones aren't dramatically better than that. So you only come out ahead with a new car if you put a lot of miles on it. But then that's still conflating "new" and "efficient" -- a 2004 Prius still gets better mileage than the new car average.

This doesn't apply to electric cars, which do use dramatically less petroleum (i.e. none), but they're mostly already made in the US, so making petrol cars cost more may actually be an environmental advantage because more people will buy electric.

People are driving drastically less.

Not without a change in the underlying dynamics including infrastructure. Used car sales and prices have dropped drastically and so people would just keep their old inefficient cars longer than ever before.

Remote working if it sticks might contribute more to car reduction.