A USB socket of the Type C design can be used for ANY of the three current USB3.2 versions: Gen1 is max 5 Gb/s data transfer speed, Gen 2 is 10, and Gen 2x2 is 20 max. What you really need to look at the the connector on the end of the cable that comes down from that front panel to plug into a mobo header.
There is a standard mobo header used for USB3.2 ports called 19-pin, and it is used for either Gen1 or Gen 2 ports - the difference is only in the capabilities of the mobo controller chip. Each such header actually contains two USB3.2 ports, so a cable plugged into one of these should be feeding TWO exterior sockets ideally. Those might both be of the same type (either Type A to Type C), or one of each. The USB people recommend that a socket and cable of Type A (the older style, but for USB3 with blue inserts, not USB2 with black inserts) can be used for either Gen1 or Gen 2, BUT may not deliver full 10 Gb/s speed on a Gen2 connection. Type C is recommended for Gen2 and definitely required for Gen 2x2.
The mobo header for a Gen 2x2 port is much different - called Type E - and requires a different cable and connector to get to an exterior socket that must be Type C. This header has only one USB 3.2 Gen 2x2 port.
So, you need to know which connector is on the end of your new case's cable, and what mobo headers you have to plug that into. If you have NO USB3 mobo headers then you will need an add-on card as suggested above. Tell us what case you got, and what mobo - maker and exact model number - and we can help you find out what things you can match up.