In Windows 11, why doesn’t pinning a sticky note to a specific desktop minimize it?

I need a sticky note tool that can be pinned to a specific virtual desktop. Requirements:

1. It must remain pinned to that virtual desktop at all times and not follow when switching to other desktops;

2. It must stay in the background or remain on top, without interfering with other operations;

3. It must not automatically minimize when the Show Desktop button on the taskbar is clicked.

I have tried several sticky note apps, but none can meet all of the above requirements. Please recommend a tool that meets these criteria.