I can reproduce the problem on my OnePlus 6 with /e/OS e-2.8-a14-20250221470208-community-enchilada. Clearing the App Lounge storage has not helped.
I have not found anything related in the /e/OS GitLab. If this problem continues, a bug report should maybe be opened, and the problem mentioned in the Feedback for v2.8 thread.
I mainly use Aurora Store with an anonymous account for my Play Store apps, so this may be a suitable workaround for now, @Weidenwiesel ?
EDIT: I use an alternative webview, so I will check whether the problem is still there if I switch to the original /e/OS webview.
EDIT 2: After switching to the original webview, installing apps did not work. When I cleared the App Lounge storage again, the problem was fixed. Switching to the alternative webview then seems to have recreated the problem. However, this could also be caused by problems with the anonymous account of the App Lounge, so I cannot really name the webview as culprit yet.
@Weidenwiesel : Do you use an alternative webview?