Reuters claims it does! Award for interesting evidence to the contrary. Bounty says 50 instead of 500 because probably nothing will come out on this ever and that money would be locked up forever :/

https://www.reuters.com/investigates/special-report/tesla-batteries-range/

Tesla years ago began exaggerating its vehicles’ potential driving distance – by rigging their range-estimating software. The company decided about a decade ago, for marketing purposes, to write algorithms for its range meter that would show drivers “rosy” projections for the distance it could travel on a full battery, according to a person familiar with an early design of the software for its in-dash readouts.

Then, when the battery fell below 50% of its maximum charge, the algorithm would show drivers more realistic projections for their remaining driving range, this person said. To prevent drivers from getting stranded as their predicted range started declining more quickly, Teslas were designed with a “safety buffer,” allowing about 15 miles (24 km) of additional range even after the dash readout showed an empty battery, the source said.

The directive to present the optimistic range estimates came from Tesla Chief Executive Elon Musk, this person said.

“Elon wanted to show good range numbers when fully charged,” the person said, adding: “When you buy a car off the lot seeing 350-mile, 400-mile range, it makes you feel good.”

Note that I can't tell from the way this is written if tesla still does this today. Bounty is awarded if any interesting evidence (doesn't have to fully convince) that Tesla doesn't do this now, or didn't at all!.