I know I mentioned it yesterday but really worth reading Sam Freedman's* Theory of Power article on Substack. There is probably a free trial.
It provides context for many of the appointments and some planned developments for an economic unit in No 10 (no, there isn't one at the moment) and the appointment of Emma Norris.
On the topic of appointments it makes sense to keep most of them within his sphere. Carping from Cabinet level potential leadership candidates will be kept to a minimum. I know that is a bit rich all things considered but PMs are brought down from within. See the efforts of Braverman, Jenrick etc.
There was also a really interesting article in the FT this morning "MPs call on Burnham to extend employer tax break for under 25s" that links to the Milburn review which will provide policy recommendations in the Autumn.
I can see why they wanted to start in September, it does seem like there has been far more thinking about what is needed than the press will give them credit for.
I haven't had anything particularly nice to say about Burnham in the past but I hope he is given time to pull this together.