Combining optical gain in direct-bandgap III-V materials with tunable optical feedback offered by advanced photonic integrated circuits is key to chip-scale external-cavity lasers (ECL), offering wideband tunability along with low optical linewidths. External feedback circuits can be efficiently implemented using low-loss silicon nitride (Si3N4) waveguides, which do not suffer from two-photon absorption and can thus handle much higher power levels than conventional silicon photonics. However, co-integrating III-V-based gain elements with tunable external feedback circuits in chip-scale modules still represents a challenge, requiring either technologically demanding heterogeneous integration techniques or costly high-precision multi-chip assembly, often based on active alignment. In this work, we demonstrate Si3N4-based hybrid integrated ECL that exploit 3D-printed structures such as intra-cavity photonic wire bonds and facet-attached microlenses for low-loss optical coupling with relaxed alignment tolerances, thereby overcoming the need for active alignment while maintaining the full flexibility of multi-chip integration techniques. In a proof-of-concept experiment, we demonstrate an ECL offering a 90 nm tuning range (1480 nm-1570 nm) with on-chip output powers above 12 dBm and side-mode suppression ratios of up to 59 dB in the center of the tuning range. We achieve an intrinsic linewidth of 979 Hz, which is among the lowest values reported for comparable feedback architectures. The optical loss of the intra-cavity photonic wire bond between the III-V gain element and the Si3N4-based tunable feedback circuit amounts to approximately (1.6 +/- 0.2) dB. We use the ECL as a tunable pump laser to generate a dissipative Kerr soliton frequency comb. To the best of our knowledge, our experiments represent the first demonstration of a single-soliton Kerr comb generated with a pump that is derived from a hybrid ECL.