I have the same problem on my iPAD Air 5th, 17.4.1. On Thursday, I turned on Developer mode as Apple help article says, to input sandbox data, it's all worked fine.
And on the Friday, May 10th tadaaa: I have no option to download any app from Appstore/Testflight, the download is eternally on start.
I did everything besides flushing device to the factory condition.
When I turn on any VPN the download is happening as usual. Seems this is country+provider issue no one going to fix.
I found similar issues reported since 2021, so draw your own conclusions.
Chat support literally said I have to call at my own expense to other country and speak in Spanish, because they can't schedule call back for me to resolve the issue. I can buy device, but I can't have a support here.
All of my work with Testflight builds is stuck for 2 days.
SELFUPDATE 20 mins later: HAH! I realized 17.5 is standing ready for install and all fixed magically after update! This stucked OS installation prevented all Appstore/Testflight downloads. Whoa.