The longitudinal coupled-bunch mode-0 instability is a significant collective effect in high-current storage rings. It appears as a coherent oscillation of the common synchrotron phase and energy deviation of multiple bunches, causing jitter in bunch arrival time and beam energy and thereby degrading timing stability, longitudinal beam quality, and the achievable stored current. Conventional mode-0 feedback systems typically use dedicated narrowband cavity filters to extract the mode-0 oscillation component and introduce a phase-shifting stage to establish the quadrature phase relation required for damping. Although effective, such implementations rely on dedicated cavity-filter hardware, which increases system integration complexity and cost. In addition, variations in the synchrotron oscillation frequency require feedback-phase adjustments to maintain optimum damping. To address these limitations, we propose a cavity-filter-free adaptive mode-0 feedback method based on the low-level RF (LLRF) system. In this method, the mode-0 component is extracted in the FPGA using digital algorithms and adaptively phase-shifted using a zero-padded FFT spectralpeak tracking algorithm. The phase-shifted signal is applied through a rotation-matrix operation in the vector modulator, providing damping of the mode-0 synchrotron oscillation via RF phase modulation. To verify the feasibility of the algorithm under no-beam conditions, an LLRF test platform was developed using parameters of the Super Tau-Charm Facility (STCF). The platform generates an equivalent BPM sum signal and implements discrete RF-cavity and beam phase-response models in the FPGA to form a self-contained closed loop. Offline tests show that, when the power levels of the first-order revolution sideband and the mode-0 oscillation sideband are −3.96 dBc and −36.49 dBc relative to the RF carrier, respectively, the system extracts a mode-0 oscillation component with a spectral peak approximately 70 dB above the noise floor. The feedback loop effectively suppresses the mode-0 sideband. For five prescribed synchrotron-oscillation frequencies, the proposed zero-padded FFT spectral-peak tracking algorithm reduces the required data-acquisition time by approximately a factor of 85 compared with a conventional FFT at the same frequency resolution, while limiting the frequency-tracking error to below 1%. The maximum deviation between the additional feedback phase calculated by the algorithm and the optimum feedback phase obtained from the manual phase scan is less than 4°, demonstrating low-latency adaptive phase adjustment for varying synchrotron-oscillation-frequency conditions.