Tesla is building battery manufacturing plant. Also, if battery availability isn't a limiting factor in car production rates, it's not a valid comparison.
Musk predicted 100 GWh of 4860 cell manufacturing in 2022. At the end of the year, it was running at an annualized rate of about 4 GWh/year in Austin, and had temporarily abandoned cell production in Berlin for an undisclosed period of time. I don't know the current capacity of Panasonic or CATL, but this gap seems significant.
Generally speaking, I would be hesitant to accept claims from any EV manufacturer that cell manufacturing capacity is not a constraint.