In the file /vendor/magento/module-checkout/view/frontend/layout/checkout_cart_index.xml
you may verify you find a block definition like below:
<block class="Magento\Checkout\Block\Cart\Crosssell" name="checkout.cart.crosssell" template="Magento_Catalog::product/list/items.phtml" after="-" ifconfig="checkout/cart/crosssell_enabled">
<arguments>
<argument name="type" xsi:type="string">crosssell</argument>
</arguments>
<block class="Magento\Catalog\Block\Product\ProductList\Item\Container" name="crosssell.product.addto" as="addto">
<block class="Magento\Catalog\Block\Product\ProductList\Item\AddTo\Compare"
name="crosssell.product.addto.compare" as="compare"
template="Magento_Catalog::product/list/addto/compare.phtml"/>
</block>
</block>
this tells you the default location in Magento installed version of your template is: Magento_Catalog::product/list/items.phtml
However, if you look into this file, you will see it does get reused for related products, upsells and in general any products listing that have no toolbar navigation.
If you intend to implement your M1 template in this template, you have to bear this in mind.
The options you have that I can see may be to check how related products or upsells products have been integrated in your site. If you find something, then, it should make sense to reuse these for crossells.