Filing is never final. Moving a note is quick on both platforms, and nothing about the note changes except where it lives.
On desktop
Drag the note from the list onto a folder in the sidebar. The folder highlights as you hover it. You can also right click the note and choose Move to Folder, which opens the folder tree including subfolders.
On mobile
Swipe a note row to the left and tap Move, in a folder or in the search results, or open the note and choose Move to Folder from the header menu. The folder tree appears as a sheet, with New Folder at the top: name it and the note moves straight into the folder you just made. Folders themselves can be moved the same way, including up to the top level.
Moving many notes at once
Select the notes first, with Cmd or Shift clicks on desktop and Select Notes from the folder menu on mobile, then move them once as a batch. If everything in a folder belongs somewhere else, moving the folder itself is faster still.
The modified date stays put
Moving is not an edit. A moved note keeps the modified date of its last real change, so it sorts in its new folder where that change put it rather than jumping to the top. The same goes for a note deleted into Recently Deleted and for one restored out of it.
Links and tags survive the move
Note links keep pointing at the right note and tags stay attached, so reorganizing does not break anything.
Shared folders
Notes cannot move between your own folders and a folder someone shared with you yet. In a folder you share yourself, your own notes move in and out as usual: moving one in shares it with the folder's people, and moving one out stops sharing it.