This paper investigates the soft-switching quasi-square-wave (QSW) technique in DC/DC SiC-based flying capacitor converter with quasi-two-level (Q2L) control establishing design guidelines for constructing high-efficiency soft-switched bidirectional converters with low-voltage power transistors. The general idea behind the soft-switching in the proposed system is based on near-CRM (critical conduction mode) operation using TCM (triangular current mode) and Q2L control with the addition of auxiliary transistor capacitances. The soft-switching process is based on a resonance between the capacitances in parallel to each transistor, and the main inductor - ZVS at turn-on is ensured through proper modulation pattern according to TCM-Q2L control, and the turn-off soft-switching mechanism is assured through the novelty in the form of adding auxiliary capacitance in parallel to each of the SiC power MOSFETs according to QSW operation. Thus, the converter can reach very high efficiency (peak at 99.5%), maintaining soft-switching for a wide operating range, using only small auxiliary SMD capacitors and a low-volume flying capacitor, leading to high power density. The presented study is based on experimental tests using a 1.5 kV model at up to 15 kW and includes the impact of various auxiliary capacitance values and optimal capacitor value selection for maximizing the converter efficiency.