To remove the “Sidebar Menu” widget from Home page you need delete it from Primary Widget Area in Appearance > Widgets.
To add categories to the sidebar on the Shop page you can do this via Appearance > Widgets as well.
Just drag “Woocommerce product categories” widget into the “Product Page Sidebar” area.
We recommend you to use Woocommerce widget for categories and not Sidebar Menu which you’re using now. There are will be spaces with “Woocommerce product categories” widget.
Thank you.
Regards,
Eva Kemp.