I consider this a bug. Is anybody else having this problem?

If your problem was indeed a bug we’d have heaps of complaints from users. So I’d tend to think more about the way you are operating Notepad++ (NPP) or the environment it’s running under.

There are some tests you could perform:

1. Open NPP without any open files, it will then have just one blank/empty tab open. Then close NPP and see if any difference occurs. If so, then maybe the open files you have open when the problem occurs have a bearing on the problem. Are they large files? Is the location of the “saved” versions on a remote/network drive and it’s taking a while for Notepad++ to get a response back that they’ve been saved?
2. Download another version of NPP, preferably the portable version. This can be installed elsewhere on your system. See how it works?
3. When you say NPP is still on the taskbar, for how long? Can you leave it a while to see if it does close eventually?
4. Presumably the NPP you have installed is from the official source (https://notepad-plus-plus.org/downloads/). Under each version a link to download a portable version is present. This isn’t really installed, rather just unzipped into a folder (not under program files). It is self contained and won’t mess with your installed version.

So we can only give you some guidance on what to search for. You will need to perform those tests, and put in some effort to help identify the reason.

Terry