According to Rik Nieuwdorp's LinkedIn Page (spotted by Timur222 on Twitter), the game has now begun development with their projects section stating "Lighting Artist on currently in production Indiana Jones title. Details will be forthcoming in the future".
This section says that Nieuwdorp began working on the game in March 2021, suggesting that MachineGames are focusing on this title, or at least in early development.
This does come as somewhat of a surprise as many are expecting the developer to announce and release Wolfenstein 3, sometime within the next year or so.
However, it could be that the development of Wolfenstein 3 is complete and all that is left is to polish up the experience and perform Quality Assurance testing.
Nieuwdorp may have also just not worked on the conclusion to the Wolfenstein trilogy if it is in development or it can't be displayed in their profile because it hasn't been officially announced yet.
Either way, what MachineGames is up to is still a secret for now, but we are expecting some details to be revealed at E3 2021 next month.
As for whether or not the game will come to PS5, it doesn't seem likely. Just today journalist Jeff Grubb confirmed that Starfield will be an Xbox and PC exclusive.
Phil Spencer also previously said that new Bethesda games will only release on platforms where Game Pass exists. However, given Wolfenstein's legacy on PlayStation, it could still come to PS5, but we don't think it is very likely.