RK3568 and RK3588 both have USB 2.0 OTG support only. as per the datasheet and this recent post on the LKML.
It’s not quite that simple, though - the controllers are set up so that one type-C OTG port runs at USB 3.1 speeds in host mode, but is limited to USB 2.0 speeds in device/gadget mode.
It also looks like the 3568 and 3588 have a lot of IP blocks in common - peripheral drivers etc. for the 3568 are likely to not require much in the way of changes for the 3588.