If you need to override ONLY some template just use <referenceBlock> in your module layout file. For example, you need to overwrite next template
ORIGINAL BLOCK in ...
Use template path hint to show the file path. This will show all the .phtml files used on page view.
To enable template hints, your environment should be development
Note: Do not enable template hint on live website
Use this one to enable template path hints https://magento.stackexchange.com/a/91240/31910
Other way to find code is to use well known IDE like ...
In this case, your only option would be to create a subclass of Magento\Quote\Model\Quote\Item\CartItemPersister and implement your changes there. This can get messy when the parent class implements a lot of private methods which usually means that you need to copy the parent class to the subclass and then add your customizations on top.