GDAL - Colourise polygon ndvi from sentinel 2-A data

Question

I am trying to take a sentinel 2-A jp2 file and along with coordinates for a given polygon, generate the colourised ndvi of that polygon and where everything outside of the polygon is transparent. I then want to convert it to a png.

Given I know where in the map the polygon is located, I got the tile from sentinel that covers that location.

I then used gdal_calc.py with the --projwin option to limit the affected area to an area that contains the polygon. From there I am capable of colourising the resulting ndvi image.

Now I want to take the coordinates that I have for that polygon

"geo_json": {
    "coordinates": [
      [
        [
          -0.5183105267238857,
          52.70755889050349
        ],
        [
          -0.5138501418205424,
          52.707355479805585
        ],
        [
          -0.5090106495574819,
          52.70424627990798
        ],
        [
          -0.5139704021925185,
          52.70204813127995
        ],
        [
          -0.5175195079000033,
          52.70175750758153
        ],
        [
          -0.5183105267238857,
          52.70755889050349
        ]
      ]
    ]

and apply them to the resulting ndvi image so that only the cells contained inside the polygon are colourised and everything outside of the polygon is transparent.

I might not be following the right sequence of commands to achieve my goal, so am open to different approaches. I also don't know which of the gdal commands I now need to use to reach my goal.

So far I have gone from taking this image:

And calculating the colourised ndvi for this section (picture from QGIS to illustrate):

The commands I've used so far have been:

docker run --rm -v /Users:/Users osgeo/gdal:alpine-normal-latest gdal_calc.py --calc="((B.astype(float)-A.astype(float))/(B.astype(float)+A.astype(float)))" -A /Users/hyprstack/Documents/gdal-test/T30UXD_20210531T110621_B04.jp2 -B /Users/hyprstack/Documents/gdal-test/T30UXD_20210531T110621_B08.jp2 --outfile=/Users/hyprstack/Documents/gdal-test/ndvi.tif --type=Float32 --overwrite --projwin 652300 5861239 692881 5835090

Which produced:

And then ran:

docker run --rm -v /Users:/Users osgeo/gdal:alpine-normal-latest gdaldem color-relief /Users/hyprstack/Documents/gdal-test/ndvi.tif /Users/hyprstack/Documents/gdal-test/color_map.txt /Users/hyprstack/Documents/gdal-test/ndvi_color.tif To produce: