they all are similar, don't worry, there's lots to get your teeth into...

So, while I'm waiting for this book to arrive, I've spent even more time "googling".

IF, you can believe all that is on the internet (?) there appears to be no standard, with regards to Bugatti's differential type. Some appear to have solid/locked rear axles, some appear to have open/live centres and some even appear to have limited slip units. I'm guessing the LSD style must have been a much later "after market" fitment, but there doesn't appear to be any hard & fast facts regarding the the solid/open differential design fitted to these particular models (Type 35 A/C, 37, 59). Possibly because some were used as race cars only while others were used as road going cars, and then, over time, parts have been swapped out by owners.
The other possibilty of course is that not all the information on the internet is correct & that some of the sources (possibly even owners), don't know.

But I will wait & read the book, see if there is any information in there

I do not know which information you read on the internet but Bugatti certainly used a standard with regards to the differential type and that is a normal differential!
NO solid /locked rear axles! At least not as long as Molsheim was involved.
I do not believe Molsheim ever used a LSD on a Bugatti before the war despite what UK Bugatti racers seem to believe. Any evidence to the contrary is most welcome.
Bugwrench