On the other hand, if the polygon does not represent a single elevation value, You can convert the polygon to a "stream" by extracting the z values from the DTM for each Vertex and creating a surface from those points ,(masked to the polygon) then run GRASS GIS r.hand, https://grass.osgeo.org/grass-stable/manuals/addons/r.hand.html to flood to 2 meters around the polygon.
r.hand - GRASS GIS manual

r.hand: Performs Height Above Nearest Drainage (HAND) analysis and flood inundation mapping with HAND method.