I do not know about 'better way' Got me beat.
A couple of ways.
Colors -> Map -> Palette Map But first make a palette with your colours. Import from a temporary image. The docs here: https://docs.gimp.org/en/gimp-palette-dialog.html
But then it will need editing, from darkest = red to lightest = yellow
Applied looks like this before and after: https://i.imgur.com/CmGwk0f.jpg
Another way
Convert the image to indexed mode, with a small number of colors. Image -> Mode -> Indexed
Open the colormap dialogue Windows -> Dockable Dialogues -> Colormap and edit the colour map replacing the various grays with colours. Another before and after. https://i.imgur.com/YYR1vzo.jpg
Then Image -> Mode and back to RGB
edit: Then thinking about your images, you probably want the gray shading incorporated, the original grayscale over the coloured in image in one of the layer modes should work.
another example, used palette map and overlay in color(LCH) mode - Just realised you are using a Mac and probably Gimp 2.8 That mode is available in Gimp 2.10
A couple of ways.
Colors -> Map -> Palette Map But first make a palette with your colours. Import from a temporary image. The docs here: https://docs.gimp.org/en/gimp-palette-dialog.html
But then it will need editing, from darkest = red to lightest = yellow
Applied looks like this before and after: https://i.imgur.com/CmGwk0f.jpg
Another way
Convert the image to indexed mode, with a small number of colors. Image -> Mode -> Indexed
Open the colormap dialogue Windows -> Dockable Dialogues -> Colormap and edit the colour map replacing the various grays with colours. Another before and after. https://i.imgur.com/YYR1vzo.jpg
Then Image -> Mode and back to RGB
edit: Then thinking about your images, you probably want the gray shading incorporated, the original grayscale over the coloured in image in one of the layer modes should work.
another example, used palette map and overlay in color(LCH) mode - Just realised you are using a Mac and probably Gimp 2.8 That mode is available in Gimp 2.10