You can manage files and folders within a project directly from the Files tab inside the project. If you already have a file open, go to Overview and click + Move to project on the right-hand side.
If the file is already part of a project, you can remove the file from the project or move it to another one by clicking on the three-dot menu.
Where You’ll See It
Select a file > Overview
If the file is in a project: shows the project name + three dot menu (Move to another project, Remove from project).
If the file is not in a project: shows Move this file to a project.
Project page > Files tab > folder or file > Three dot menu
Files: Copy link, Open source, Move to another project, Archive (if applicable), Remove from project.
Folders: Rename, Copy link, Open source, Move to another project, Remove from project.
Permissions & Edge Cases
Move to project disabled: If you lack permission, the button is disabled with an informative tooltip.
You can move into a project when (Microsoft): from your personal Drive, from SharePoint sites you can access, or from the Burai Projects SharePoint site.
Google: Once a file is in a project, only the organizer (project editor) can remove it.
Summary / Next Steps
Use Move to another project from either the File page or the Project’s Files tab. Confirm permission changes, then track progress in the corner indicator.