<p>Windows has its 3D Builder software which upon importing an image, converts it to a heightmap of the image, aka turning it to a 3D model that can be saved as an stl.</p>
<p>Does Linux have software with similar properties that takes a black and white image and turning it into a 3D heightmap model?</p>

FreeCAD can import JPG (and IIRC TIFF and PNG as well) image files and produce a lithophane type height-map based on the brightness of each pixel.  I'd be rather surprised if other 3D CAD software aimed at the 3D printing user base couldn't do the same.  Most of the common free-to-use 3D CAD packages have Linux versions; FreeCAD certainly does (I use it on Kubuntu 20.04, and it should work on any recent version of any flavor of Debian-based Linux, if your hardware meets it requirements).