Every day dozens of "breakthroughs" emerge. 0.01% end up actually being something. This can only be seen in retrospec. Though, being a startup with nice-looking PR material is almost 100.0000% sign it's a con.
To be fair, it's most likely one of the big players with big R&D (think about Panasonic, more recently Samsung, or even more recently Tesla) make the best progress. It's always possible a small startup or a university doing research comes up with the killer recipe (which then takes 5 to 20 years to make into production), but the odds when seeing a press release is in ppm range.
"Solid state" refers to using solid electrolyte. Yes, we all agree the flammable organic solvent in li-ion batteries sucks, but there is lot more to batteries than just the state of the electrolyte being solid or liquid. Solid electrolyte li-ion was a big research subject in 1990's, it never worked out commercially but the term "LiPo" originally coined to describe it was repurposed by marketing to describe bog standard wet electrolyte cells.
If a significantly better "breakthrough" battery emerges, it may or may not have solid electrolyte, only the result matters, and this is measured on being actually manufacturable, $/kWh, calendar fading and cycle life, $/kWh per product lifetime, Wh/kg, W/kg, and sometimes Wh/dm^3 and W/dm^3.
A significant part of solid electrolyte "not working out" is due to the fact that liquid electrolyte is working quite fine. Solid version would need to be significantly better.