I doubt that there's actually a substantial impact on battery cell production. Might be on rack-mountable batteries containing those cells. But setting that aside:
Panasonic plans to expand lithium-ion cell
Non-rechargable AAA batteries are typically alkaline, and rechargeables are typically NiMH, not lithium-ion.
EDIT: Looking at a handful of rack-mount lithium-ion batteries on Amazon price history using camelcamelcamel, prices are either unchanged or very slightly up. Could be Panasonic looking to get into the news, but it's not clear to me that there's a shortage of even rack-mount lithium-ion batteries.