Where do web parts reside when creating them on a modern page? As for example, I created a Quick Links web part on a page A (created using the Modern Site Page template), can I add the same web part on a page B (created using the Modern Site Page template). I do not see these web parts anywhere on the site contents.
All modern web parts available on modern web parts are through Microsoft and there is no web part gallery like classic SharePoint. Custom SPFx web parts are available either through Tenant App catalog or SharePoint app catalog.