I'm having the same issue
I can connect to the PlayMemories store on both my phone (and Mac) yet when I try to download the TimeLapse app on the camera, I keep getting presented with the PlayMemories log in screen (which BTW takes aaaaages to re-log in and verify each time).
Once i've logged in (and verified via 2FA) I try to purchase the TimeLapse app and when it tries to take me to the payment screen, it asks if I have a PlayMemories/SonyID > so again I have to log-in and verify, and nothing happens...no purchase...no download.
It seems to just go back to the PlayMemories store.
I'd really like to buy the TimeLapse app (despite it being a bit expensive @ $9.99) but Sony doesn't seem to want my money