The password prompt is system-modal, making it annoying to use
Here's a user story:
Andy wants to use a password manager to store his password for an account in the Online Accounts list. When it’s time to log in, Andy clicks the account and a system modal dialog appears asking for a password. Andy would like to click the account in the password manager and copy the password, but he can’t, because the dialog is system modal. So instead, Andy grumbles, dismisses the dialog, copies the password, and then tries to get the dialog to reappear before the copied password is auto-cleared from the clipboard. Andy also wonders why the system modal dialog is not visually consistent with the Online Accounts application at all.
Yes, this is a bit snarky, but there’s a reason that Microsoft deprecated system modal dialog boxes decades ago. The fact that GNOME supports this grotesque anti-pattern and NetworkManager uses it does not justify using it in anything else.
I suppose this could be seen as a bug in GTK or gnome-shell or whatever component implements the password prompt as an actual system modal dialog instead of something reasonable, but I personally find this issue to be more annoying in gnome-online-accounts than in any other GNOME application.