No. Sticky Notes is part of Windows and does not run on Linux, but your notes are already synced to your Microsoft account and open at onenote.com/stickynotes in a browser.
Sticky Notes by Microsoft · Notes & PDFs · No way to run it
Sticky Notes ships with Windows and there is no Linux version. It is not sold separately and cannot be installed
anywhere else.
Your notes are not stuck on the old machine, though, which is the part most people worry about. As long as you were
signed in, Sticky Notes syncs to your Microsoft account. Go to onenote.com/stickynotes in Firefox or Chrome on
Linux, sign in with the same account, and every note is there. They also appear in Outlook on the web and in the
OneNote apps on a phone. Do this once before you wipe the Windows PC and you will know nothing was left behind.
For day to day use on Linux, a browser tab is a poor substitute for little yellow squares on your desktop. Most
Linux desktops have a small sticky notes applet available in their app store, and any simple notes app covers the
same job. Joplin is the more capable choice if the notes are worth keeping and searching.
Already installed on most systems. Opens instantly, remembers unsaved scraps, and does nothing else.
Your files: Plain text files only.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need Sticky Notes. Everything else you do can move.