How do SOCs transmit at a higher speed than the internal clock?
Modulation is not typically done at the carrier frequency, but rather at a lower frequency and upconverted.  In the era of digital modulation, it's not even uncommon for the key processing to be done in the context if IQ signals centered on a frequency if 0 Hz.

Upconversion does require a local oscillator, but this is a sine wave rather than square, and only drives a small part of the radio circuitry, not the chip in general.  Typically today that would be synthesized in relation to a convenient frequency crystal.