We present a near-infrared optical parametric chirped-pulse amplifier (OPCPA) and soft X-ray (SXR) high-harmonic generation system. The OPCPA produces few-cycle pulses at a center wavelength of 800 nm and operates at a high repetition rate of 100 kHz. It is seeded by fully programmable amplitude and phase controlled ultra-broadband pulses from a Ti:sapphire oscillator. The output from the OPCPA system was compressed to near-transform-limited 9.3-fs pulses. Fully characterized pulse compression was recorded for an average power of 22.5 W, demonstrating pulses with a peak power greater than 21 GW. Without full temporal characterization, high-power operation was achieved up to 35 W. We demonstrate that at such high repetition rates, spatiotemporally flattened pump pulses can be achieved through a cascaded second-harmonic generation approach with an efficiency of more than 70%. This combination provides a compelling OPCPA architecture for scaling the peak power of high-repetition-rate ultra-broadband systems in the near-infrared. The output of this 800-nm OPCPA system was used to generate SXR radiation reaching 190 eV photon energy through high-harmonic generation in helium.