The cheapest Tesla is three times the new price of the car my wife currently drives (£38,000 vs £12,500). That kind of implies the Tesla is a lot more carbon intensive than buying a cheap car, even over its lifetime.
You just need to look at the dance the price of oil and the health of the economy go through to realise money and energy are deeply intertwined. It’s not obvious to me that we can completely decouple them.
The price of oil itself has no correlation with carbon output. (Total production numbers might tell you something, but that is only vaguely related to price in market economics, given the competing forces of supply and demand. Total usage numbers would tell you a lot more, but isn't a statistic even tracked by economics and if it has any correlation on price depends on the type of demand [elastic versus static] whether it is following/lagging or pushing the price.)
Sure money and energy can be considered intertwined, but not all energy is carbon, don't forget that as much as business tries to underprice it, a lot of the energy reflected in a supply chain is labor (which admittedly people do also produce carbon, but exhalation effort is not something I've ever seen properly reflected in someone's wages).
So again: higher prices in EVs and EV supply chains absolutely does not correlate with carbon costs. EVs generally have less material because a) weight matters a lot more, and b) fewer moving parts / simpler drive trains.
Price differences likely reflect other market realities such as supply/demand and things like perceived luxury.
All in, over their lifetimes, those non-fashionable solar panels will save far more carbon than the tesla. So unless you have already maxed your solar options, the tesla is more fashion statement than "green" decision.