Sorry for the delayed response on this. CY8C6247 does not have a dedicated SDHC support; instead SDIO host controller was implemented using UDBs. I hope now the CY8CKIT-062 kit operation makes sense.
Instead, I would recommend using CY8C62x8, CY8C62xA family in your new design which has dedicated SDHC interface for you to interface the WiFi/BT solutions from Cypress. Reference kit: https://www.cypress.com/documentation/development-kitsboards/psoc-6-wi-fi-bt-prototyping-kit-cy8cproto-062-4343w