Yes.
Have you rebooted the system? If that change was made after these issues began, then it may require a reboot to clear things out. Restarting the system can fix a lot of odd issues.
Perhaps it may be a bug or new feature with Sequoia. I know I don't have that problem with Ventura and have not installed Sequoia on my unmanaged Mac yet. Apple may be pushing for updates to be installed more quickly. Unfortunately most of the Macs I support are being managed which can change how macOS behaves, but I haven't seen the pop-up on them.
I believe Apple even changed the update notifications which appear on the upper right so that it is no longer possible to just close them in Sequoia (perhaps even Sonoma)....that the notification only provides two options these days and if the notification is clicked it will bring up that pop-up where you need to authenticate.
I'm not sure I will have the time or access to a system where I can experiment a bit.
I also like to install update patches on my own terms...sometimes it just isn't convenient to disrupt my work and other times I don't want to risk dealing with any issue that may arise from an update (rare, but it can happen), plus I like to wait a bit to make certain people are not having issues with a particular update (again rare with macOS, but it has happened).