It's quite tricky actually.

There's other negative externalities from car usage apart from the energy usage, like tire and brake dust, congestion, accidents, and road wear. And using up limited space in cities for parking. Etc. etc.

Even if you only wanted to tax energy usage, that clearly correlated with the amount of fuel or electricity used. Taxing liquid fuel is common and a sensible choice, however you can't slap on a big tax on electricity in general since if anything we want to encourage electricity use in favor of fossil fuels (e.g. heat pumps powered by zero-carbon electricity instead of gas heating, or indeed EV's instead of ICE vehicles). And arguably for electricity, it would be better by slapping a CO2 tax on the producers (or some roughly equivalent scheme like cap-and-trade) rather than taxing electricity generally.

And of course, if you want to tax by miles driven, that then gets into all kinds of problems how to track that in a way that doesn't enroach on people's privacy. Say, checking the odometer during yearly inspections?

So where does that leave taxing EV's? Maybe a flat yearly fee based on the weight isn't that terrible, and it's at least cheap to administer and doesn't leave much space for cheating. Although that is of course very unfair to those who live out in the boonies where parking space is not at a premium and drive very little.

You can slap a tax on the car. You simply take energy used/miles driven and that's your multiplier for a yearly vehicle tax. It could be collected by insurance companies (that usually require you to submit the miles driven anyway) on behalf of the government .

As for the other things, such as congestion, I believe it when I see proof that there is a big difference between cars. Even if there is, the priority right now should be energy efficiency, because reducing CO2 emissions is fairly urgent.

I fully agree reducing CO2 emissions should have a high priority. Which for fossil fuels would mean a quite substantial tax on the fuel volume, but for EV's it's trickier since electricity is used for many other things, and electricity production is already taxed for CO2 emissions (or cap and trade etc). There's no particular reason, from an emissions perspective at least, why electricity for EV's should be taxed higher than, say, for domestic use. If anything, an extra tax on electricity could be counter-productive if it causes more people to prefer ICE cars.

Which implies that a vehicle tax should then be primarily concerned with non energy use types of externalities. And maybe generally funding road construction, and so on. Probably a lot of that is more accurate if the tax is a function of distance driven than a fixed cost, true, assuming you can reliably get that information in a privacy compatible way.

No why should you ignore road deterioration? Road deterioration is Weight^4