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The 21000 device you find on the CY3212 is a universal chip that can be used to debug any device from the CY8C21x34 family. You can develop a project for any device in this family and run on the device. Just select the actual device number, say CY8C21434 in the programmer and you will be able to program the 21000 device.
On the other hand, CY3212 is for the CSR method of capacitive sensing. This method is not supported by the latest PSoC Designer version. The latest PSoC Designer only supports CSD method of cap sensing. If you want to test the 3212, you will have to install the older PSoC Designer 4.4 version. I have some example projects for CY3212, but I am not able to attach files in the forum here. I can email you the files if you want them.
Module used with the board which have been handed over to you is no longer recommended by Cypress. I strongly recommend you to get in touch with Cypress University Manager and ask for an updated board. They'll provide you the same and the relevant projects which need to be used.