Lasers that combine narrow linewidths with rapid tunability are critical for applications such as coherent optical ranging, distributed fiber-optic sensing, and precision spectroscopy. Despite significant progress in integrated laser technologies, the concurrent realization of low phase noise and frequency agility on a single integrated platform remains challenging owing to a fundamental architectural trade-off: conventional integrated laser designs typically suppress phase noise via high-Q resonators, yet the extended photon lifetimes inherent to such resonators intrinsically constrain tuning speed. Here, we address this noise-agility trade-off by introducing a laser architecture that achieves ultralow phase noise and ultrafast tunability simultaneously. Rather than relying on ultrahigh-Q resonators for self-injection locking, our design employs strong synthetic feedback within a Pockels-tunable, resonator-enhanced distributed Bragg reflector to suppress phase noise. As a proof of concept, we demonstrate a hybrid integrated laser with a short-term linewidth of 29 Hz, realized using a lithium niobate external cavity with a loaded Q of only 0.62 million. The adoption of a moderate resonator Q relaxes the photon-lifetime constraint on tuning speed, enabling sub-exahertz-per-second tuning rates and a chirp nonlinearity as low as 0.14%. Leveraging this laser, we implement a frequency-modulated continuous-wave LiDAR system that achieves a relative ranging precision of 1.7 × 10⁻⁴ at a measurement rate of 1 MSa s⁻¹, without requiring complex chirp linearization techniques. We further demonstrate fiber-optic acoustic sensing capable of detecting sub-με dynamic strain, underscoring the platform's versatility for high-speed precision optical measurements. Our work provides a route toward cost-effective yet high-performance sensing and metrology systems.