Looks like the Williams family were offered the opportunity to stay on (what they are saying to the press) and it was their choice to step away. Probably better than being pushed at the end of the season.
Racefans had an article recently about the sale trying to dig in to find the new owners with some interesting links.
In my opinion, this was all done in the board room when they sold, even them handing over the reins now. They were never going to keep the Williams at the helm given the recent (years) run, and I would be very surprised if it wasn't a condition of sale. Dorilton have said they will provide clarity on who will take over the day to day before next weekend, so clearly someone is standing in the wings.
You can see from the comments from Claire in the past that they never wanted to leave the team, and she said in a Sky interview that she wanted to stay at the helm.
I know it's a bit of a romantic story of them leaving on their own accord and "walking away", but in a business sense the Williams family involvement in running the team doesn't predict success and hasn't done for years, and so any buyer would be mad to keep them running things. They were pushed (or forced to resign if you prefer that language).
In a lot of businesses, when acquired, a long handover with maintaining the status quo is beneficial for a number of reasons. But given the last few years and static regs for next year, it makes sense to make the changes now, mid season, use the rest of the season to get the lay of the land, and then they still have a year next year to sus things out before the big reg change.