Next-generation computing clusters require ultra-high-bandwidth optical interconnects to support large-scale artificial-intelligence applications. In this context, microring modulators (MRMs) emerge as a promising solution. Nevertheless, their potential is curtailed by inherent challenges, such as pronounced frequency chirp and dynamic non-linearity. Moreover, a comprehensive understanding of their coherent dynamics is still lacking, which further constrains their applicability and efficiency. Consequently, these constraints have confined their use to spectrally inefficient intensity-modulation direct-detection links. In this work, we present a thorough study of MRM coherent dynamics, unlocking phase as a new dimension for MRM-based high-speed data transmission in advanced modulation formats. We demonstrate that the phase and intensity modulations of MRMs exhibit distinct yet coupled dynamics, limiting their direct application in higher-order modulation formats. This challenge can be addressed by embedding a pair of MRMs within a Mach-Zehnder interferometer in a push-pull configuration, enabling a bistable phase response and unchirped amplitude modulation. Furthermore, we show that its amplitude frequency response exhibits a distinct dependency on frequency detuning compared to phase and intensity modulations of MRMs, without strong peaking near resonance. Harnessing the ultra-fast coherent dynamics, we designed and experimentally demonstrated an ultra-compact, ultra-wide-bandwidth in-phase/quadrature (I/Q) modulator on a silicon chip fabricated using a CMOS-compatible photonic process. Achieving a record on-chip shoreline bandwidth density exceeding 5Tb/s/mm, our device enabled coherent transmission for symbol rates up to 180Gbaud and a net bit rate surpassing 1Tb/s over an 80km span, with modulation energy consumption as low as 10.4fJ/bit.