No, that's the purpose of pinned tabs. If you don't wish to have the tabs shown in all windows but still want easy access, bookmark many tabs with shift-command-D and you can open them with a single click.

No, that's the design intent of pinned tabs. They are pinned to the app and not a window / document. 

If you don't wish to have the tabs shown in all windows but still want easy access, bookmark many tabs with shift-command-D and you can open them with a single click.