Sony Interactive Entertainment registered the Soho Engine brand in Europe. See the record at this link.
It is difficult to imagine what exactly that is. Considering the name, it is possible that some Sony studio has developed its own engine, as was the case with Guerrilla Games’ Decima Engine with Horizon Zero Dawn (and that was also used in Death Stranding).
That said, Team Soho, also known as SCEE Internal Development Team or SCEE Studio Soho, was an internal studio located in Soho, London. Among the games developed by this team, is The Getaway of the PS2. That said, it is possible that this engine has some relationship with that past, or some homage. Fans also speculate that it might be something related to London Studio, which developed games like the ones in the series SingStar and more recently Blood & Truth for PS VR.