Adding Web Part document library to my site using powershell

Yes, it's possible to add a web part to a page using PnP PowerShel

Example

Add-SPOWebPartToWebPartPage -ServerRelativePageUrl "/Pages/PnPPage.aspx" -Path "D:\PnP\NewWebPart.dwp" -ZoneId "WebPartZone2" -ZoneIndex 0 

Note: you can get the .dwp file by exporting the web part manually, but the document library doesn't have the export option, so try to export it as mentioned at Unable to find the export web part option

Check the details steps,

• Adding Web Parts To SharePoint Pages Using Pnp Powershell
• Adding Web Part To A SharePoint Online Page Using PnP Core CSOM Library
• Webpart Provisioning to SharePoint online by PowerShell

If you are looking for adding a web part to web part gallery, check Deploy pre-configured web parts to web part gallery