The simplest way to determine how any US tax-exempt nonprofit/foundation is using its funds is by reading the annual Form 990. Since Archewell received tax exemption status in 2020, there isn’t a Form 990 publicly available yet. The determination letter says their tax year ends on 31st December, so their 990 for 2020 was due on 15th May 2021.
Once the Form 990 is available (from the IRS, Charity Navigator, GuideStar and probably other places, including their own website), it will be possible to determine how much money Archewell received and how it was spent.
Link to Archewell on GuideStar
I also couldn't find any evidence that the Sussexes had donated 'personal' money to any charities. The donations in their name came from The Royal Foundation (before it was split), Archewell, from profits following their wedding and from sales of the Grenfell cook book. I couldn't find a source for the bush fires donation, however as it came before the split (and before the funding from Prince Charles stopped) I doubt it was 'personal' money.
I'm sure if there is evidence the charity donations were made from 'personal' money, someone will be able to find and post the sources.
Regardless, the fact that charities received much needed funding is the most important thing.