The current battle for electric batteries is cost, not energy density.
LFP and sodium batteries are less dense that non-solid state lithium ion batteries but they are good enough to be used in standard version of Model 3 or Model Y and those are best selling ev cars.
Energy density is good enough, durability is good enough, what matters is lowering the price.
A battery with higher energy density but without lower price is not competitive.
Toyota still doesn't have a high volume electric car. Lack of batteries is not the cause of that but Toyota's own decisions.
Even if they get a slightly better battery, they still need to design a good ev car and that's way more to that than replacing gas tank and engine with a battery and motors.
Furthermore, you don't just mass produce ev batteries. Panasonic was struggling and loosing money for several years making batteries for Tesla. When Tesla decided to make batteries themselves, it also took them years to go from 0 to a significant number of batteries.
Idemitsu doesn't seem to make ev car batteries so I don't see how the could possibly have meaningful production in 2 years.
Furthermore, going solid state is only an incremental improvement of a component of the battery. It has the most economic value when applied at scale. So it would make most sense to license this technology to existing high volume manufacturer like LG Chem or CATL.
The realities of volume production vs. cost make it very unlikely you can just compete with CATL and LG Chem making 1/100 of their volume even if your battery is slightly better.