You have "shapes". I assume your image has separate parts that can easily be selected, NOT a complex photo from where no single item is easy to select for individual processing.
Step 1: So, select your shapes which you want to get the same color and move them to same layer, if they are in separate layers. Keep those shapes selected and be sure that nothing else is selected.
Step 2: Open Colours > Curves. Adjust the curve ends so that you have a straight absolutely horizontal line at y=128. That turns all selected to middle grey.
Step 3: Open Colours > Colourise an adjust the wanted color
This can be done separately for all shapes. => more repeating adjustments, but no need to move stuff between layers.
You can cut a shape from a layer and paste it accurately into the same place on another layer, if you do not lose the selection between cut and paste. If possible, select a little larger ara than the absolute minimum => no errors due the antialiasing.