The radar isn't using the entire 0 Hz to 60 GHz band, it will be using something like a few GHz or sometimes much less. i.e. 60-64 GHz
Also much of the processing isn't done on general purpose processors but in FPGAs or ASICs which can do lots of the parallel computation very fast.
For comparison 802.11ac has a max of 120 MHz channels, and that's cheap and everywhere these days (but runs on 5 GHz).
There are lots of basically tricks to reduce the amount of data in successive stages so that the processing is quite possible.
E.g. for 802.11a/n/c the CARRIER is in the 5.x GHz band but the modulated signal BANDWIDTH will be one of 20, 40, 80, 160 MHz around a central frequency [0]. The 'base' 20MHz bandwidth at best performance (signal to noise ratio) will be able to modulate (encode) at a raw 54Mbits/second.
Intel publish [1] an easy-to-read set of tables that show the relationships between standards, frequencies, bandwidths, MIMO, and modulation schemes.
[0] simplified - actually there is a (frequency-hopping or direct sequence) spread-spectrum method
[1] https://www.intel.com/content/www/us/en/support/articles/000...