Intense laser-driven proton pulses, inherently broadband and highly divergent, pose a challenge to established beamline concepts on the path to application-adapted irradiation field formation, particularly for 3D. Here we experimentally show the successful implementation of a highly efficient (50% transmission) and tuneable dual pulsed solenoid setup to generate a homogeneous (laterally and in depth) volumetric dose distribution (cylindrical volume of 5 mm diameter and depth) at a single pulse dose of 0.7 Gy via multi-energy slice selection from the broad input spectrum. The experiments were conducted at the Petawatt beam of the Dresden Laser Acceleration Source Draco and were aided by a predictive simulation model verified by proton transport studies. With the characterised beamline we investigated manipulation and matching of lateral and depth dose profiles to various desired applications and targets. Using an adapted dose profile, we performed a first proof-of-technical-concept laser-driven proton irradiation of volumetric in-vitro tumour tissue (SAS spheroids) to demonstrate concurrent operation of laser accelerator, beam shaping, dosimetry and irradiation procedure of volumetric biological samples.