Hi, you can download monthly statements in the format Quicken uses from the web. There is a support article on how to download/export the statements and the supported formats,
https://support.apple.com/en-us/HT211236
Daily transaction integration is not a method currently supported by the Apple Card App in the Wallet. My personal opinion is that this is not permitted because of the tight privacy and security integration of the Apple Card with the iPhone.
Apple welcomes feedback and suggestions for new features. Here is a link to provide feedback to Apple on the topic of integration with financial/accounting apps,
https://www.apple.com/feedback/apple-pay.html
In the Product Category drop down please select Apple Card and provide your feedback and suggestions. Apple promises to read all feedback provided, but cannot reply individually to the feedback provider. I hope this helps.