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I think it's not moving by using XML, Because It's commenting in module-catalog/templates/product/list.phtml file.

<?php echo $block->getToolbarHtml() ?>

Also it's define in module-catalog/view/frontend/layout/catalog_category_view.xml category.products.list block

<referenceContainer name="content">
    <block class="Magento\Catalog\Block\Category\View" name="category.products" template="Magento_Catalog::category/products.phtml">
        <block class="Magento\Catalog\Block\Product\ListProduct" name="category.products.list" as="product_list" template="Magento_Catalog::product/list.phtml">
            <container name="category.product.list.additional" as="additional" />
            <block class="Magento\Framework\View\Element\RendererList" name="category.product.type.details.renderers" as="details.renderers">
                <block class="Magento\Framework\View\Element\Template" name="category.product.type.details.renderers.default" as="default"/>
            </block>
            <block class="Magento\Catalog\Block\Product\ProductList\Item\Container" name="category.product.addto" as="addto">
                <block class="Magento\Catalog\Block\Product\ProductList\Item\AddTo\Compare"
                       name="category.product.addto.compare" as="compare"
                       template="Magento_Catalog::product/list/addto/compare.phtml"/>
            </block>
            <block class="Magento\Catalog\Block\Product\ProductList\Toolbar" name="product_list_toolbar" template="Magento_Catalog::product/list/toolbar.phtml">
                <block class="Magento\Theme\Block\Html\Pager" name="product_list_toolbar_pager"/>
            </block>
            <action method="setToolbarBlockName">
                <argument name="name" xsi:type="string">product_list_toolbar</argument>
            </action>
        </block>
    </block>
</referenceContainer>