An estimate last year claimed Tesla's costs were ~$160/kWh[1]. This article suggests by end of next year, <$100/kWh. In percentage terms that's a big improvement, but even going by last year's estimates, only $8k out of the $40k price tag of a standard Model 3 is actually accounted for by the battery. So if that $8k drops to $4k, I can imagine the car price dropping to say $35k. But not more than that.
[1] https://insideevs.com/news/400529/tesla-battery-costs-droppi...