While we are able to export other objects, and can see Notes in the system under Contact records, Data Loader exports only headers and no records under Export All. We are using the "Notes" and "Files" related lists due to deprecation of Notes and Attachments. Thanks.
This means You have enabled the advanced note and content files. Once this is enabled in your organization, Files uploaded to the Attachments related list on records are uploaded as Salesforce Files, not as attachments.
Notes related list will always upload ContentNote object i.e. advanced notes. Notes via Notes and attachment will create the record in Note object. Both are different.
So, While exporting you need to execute the export on the ContentNote object. The ContentNote object will contain all the notes that have been uploaded via Notes related list.
You can browse these links for more details:-
As an admin with “Modify All Data” you can export any classic Note record simply using Data Loader. However, with ContentNote and ContentVersion you can only export the records that are explicitly shared with you or that you own.
This means that even as an admin that using Data Loader is far more difficult to export all the ContentNotes and ContentVersions in your org. Lame-sauce.
Hope it helps you.