Nick here from Shopify. Great question!
In regard to adding additional checkboxes to the Newsletter sign-up form or to the cart page, specifically, the checkbox function is unable to gather or store the information that is required under the GDPR, so it would not provide any meaningful benefit to add it to your site. This means that adding the checkbox remains as an unsupported customization under the Shopify Design Policy With that being said, if you would still like to move forward with a double opt-in checkbox, you can do so and your best bet would be to have something custom made by a Shopify expert as a small task. You can see the small task expert directory from here.
Something else to note is that Shopify does what it can to set you up for success, there are also steps you will need to take on your own. If you have legal questions specific to your obligations under the GDPR, your best next step would be to consult with a local lawyer who is familiar with data protection laws in your locality. For some more information on GDPR in general, Shopify created a helpful document with some details about it, which you can read here.
I hope this helps and points you in the right direction for the best next steps with this.
All the best, Nick