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In the past decade, remarkable advances in integrated photonic technologies have enabled table-top experiments and instrumentation to be scaled down to compact chips with significant reduction in size, weight, power consumption, and cost. Here, we demonstrate an integrated continuously tunable laser in a heterogeneous gallium arsenide-on-silicon nitride (GaAs-on-SiN) platform that emits in the far-red radiation spectrum near 780 nm, with 20 nm tuning range, <6 kHz intrinsic linewidth, and a >40 dB side-mode suppression ratio. The GaAs optical gain regions are heterogeneously integrated with low-loss SiN waveguides. The narrow linewidth lasing is achieved with an extended cavity consisting of a resonator-based Vernier mirror and a phase shifter. Utilizing synchronous tuning of the integrated heaters, we show mode-hop-free wavelength tuning over a range larger than 100 GHz (200 pm). To demonstrate the potential of the device, we investigate two illustrative applications: (i) the linear characterization of a silicon nitride microresonator designed for entangled-photon pair generation and (ii) the absorption spectroscopy and locking to the D1 and D2 transition lines of 87Rb. The performance of the proposed integrated laser holds promise for a broader spectrum of both classical and quantum applications in the visible range, encompassing communication, control, sensing, and computing.