We illustrate the concept of PRIMAGAL, a proposed survey of polarized dust emission with the PRIMAger instrument in the Milky Way Galactic Plane to quantify the role of magnetic fields in the formation, evolution and demise of dense molecular clouds and filaments, and assemble the ultimate SED atlas of dense cluster-forming clumps. This survey will determine the strength and orientation of magnetic fields towards several thousands of filamentary clouds in a wide range of linear masses, column densities, evolution, star-formation rates and efficiencies, and Galactic environments, addressing for the first time in a statistically significant fashion the role that magnetic fields play in shaping the formation, evolution and fragmentation of dense ISM filaments down to a minimum scale of 0.4 pc up to 8 kpc distance from the Sun. In parallel to polarization mapping, the possibility to use PRIMAger's hyperspectral channels will unlock free access to narrow-band photometric imaging in the so far unexplored 24-70 μm wavelength range. This will allow us to assemble, in synergy with already existing surveys with Spitzer and Herschel (among others), the complete and ultimate atlas of Spectral Energy Distributions (SEDs) of dense clumps in the Galaxy, constraining the physical and evolutionary parameters of hundreds of thousands of these cluster-forming structures. A full Galactic Plane survey within |b| ≤ 1deg (a total of 720 sq. deg.) with a 5 σ sensitivity of ∼1.5 MJy/sr in 183 μm polarized emission, can be executed by PRIMAger in ∼400 hours....