The note attributes (aka "cart attributes") data is store in the field custom_attributes of the Shopify Abandoned Checkout data.

Selecting this field in the app will export all note attributes per order in JSON format.

To only extract specific attributes and place them in separate columns, you can use a formula like this under the Calculated Fields section:

search_attributes({{ custom_attributes }}, "Shipping-Date", search_key="key")

You can basically just copy/paste this formula and just replace "Shipping-Date" with the name of the attribute you want to pull.

Here's a screenshot of what this looks like in the app:

And here's where you can find the attribute names in the Shopify Admin:

Sample output when exported: