Not quite. Net migration is significantly down but more people are still arriving in the UK than leaving.
We know that 57% of those leaving originally came to the UK to study - so their stay in the UK was never intended to be permanent - they completed their studies and then went home.
We also know that there hasn't been a recent increase in emigration amongst British nationals.
There is some evidence that, amongst skilled workers, the highest-paid "skilled worker" migrants are more likely to leave than lower-paid ones. We don't have data on the reasons for this, but anecdotally, I know a few families that have left due to concerns about the rise of the far right and fears about changes that a Reform government might make to indefinite leave to remain etc. The higher earners inevitably have more options to choose from.
The main reason behind the fall in net migration isn't an increase in the number of people leaving the country but a fall in the number coming in. This is true across most categories of immigration. Fewer asylum applications. Fewer small boat arrivals. Fewer students. And fewer people coming for work.
There are obviously legitimate questions about whether government policies, and the wider political climate, might be contributing to the greater likelihood that highly skilled/high earning migrants might choose to leave. We know a lot of people who fall into this category and I do know that the hostile environment/anti-migrant sentiment isn't making them eager to stay.