Just spoke with a CS rep and was asked to post this here.
My Beta Desktop app downloaded the WoW: Shadowlands Alpha client (unprompted, I might add) and does not allow me access to the game through the BNet app. When using the file explorer to open the game client, it presents as the Version 9.0.1 (34003) (Beta x64) Apr 8 2020 build on it. If I try to log in, it only gives my WoW1 account the option to enter, and when it does enter, there are the typical PTR realms listed in red and inaccessible. CS Agent checked, I am not in this current Alpha wave of invites. I was previously in the Battle for Azeroth Alpha.
If anyone else experiences this error, please document your experience down below. Thanks.