Anyone who thinks this is not a decision from the mother company is naïve and don't know how corporate world works. This percentage of layoffs is not happening without the approval of Sony or from Sony directly.
They got rid of a third of their manpower, half of it moved to other SIE places.
Bungie now said that Lightfall underperformed and they were in the red, so even if TLS was very successful they had to do this. We also know TLS and Marathon got delayed. A few months ago when talking about Bungie Totoki complained about gamedevs not being disciplined enough about meeting budgets and deadlines plus about financial sustainability.
As subsidiary Bungie reports to the SIE CEO, who is also in Bungie's board of directors -like other SIE top people- since the acquisition, and now is also CEO of the SIE Studios Business Group that includes Bungie and PS Studios plus their non-gaming adaptations.
So yes, SIE/Sony must not only approved but also pretty likely decided that Bungie had to get rid of a third of their manpower, sending half of that people to other SIE teams.
In fact, I bet that inside Sony/SIE Totoki was the one who mandated it. Because Hermen proved to have a lot of patience with several projects: he allowed Arrowhead to have a 5 years delay with Helldivers 2. When he became CEO saw the TLOU1 remake and didn't like it but let it happen. Gave delays to many other games that pretty likely needed it and ended being great, like TLOU2, GoWR, HFW, GT7, Helldivers 2 etc. when other people could have just told them to release the games half baked to don't miss the milestone.