Heatmap with Contour Polygons

I have point data off the coast of Oahu. Someone else used these same data to create two polygons (approximated by me in the figure below with the green and red hand-drawn boundary lines). I believe his polygons were density-based. I also believe he used a Quartic Kernel with a radius of 1 km around each point and perhaps a 1 km-square pixel size. He cited Silverman (1986, p. 76, equation 4.5, which I believe refers to the book “Density Estimation for Statistics and Data Analysis”). I am attempting to reproduce his two polygons using QGIS 3.18 with Windows 10. I could try using R. The figure below shows the purple and black contour polygons QGIS returns for me with a similar fake data set. The two purple lines north and east of Oahu came with the base map and probably represent bathymetry. They can be ignored.

Here is a link to my fake data in CSV format and my resulting QGIS files:
enter link description here I hope this link works for others. I have never shared a Google Drive link on StackExchange and do not know whether I am doing it correctly.

    1. fake_points_oahu.csv
         a. raw data
    2. fake_points_oahu_utm (.shp, .dbf, .prj, .shx) 
         a. vector point layer 
    3. fake_points_oahu_utm_tif.tif
         a. greyscale heatmap of points
    4. fake_points_oahu_utm_tif.tif.aux.xml
         a. purpose unknown
    5. fake_points_oahu_heatmap_screenshot.png
         a. screenshot of heatmap
    6. fake_points_oahu_contour_polygons (.shp, .dbf, .prj, .shx)
         a. contour polygon layer - I think the color here is orange not purple

I have hand-drawn approximate boundaries of the original green and red polygons I am hoping to obtain. The original green polygon boundary line was labeled “> 1 per km density”. The original red polygon boundary line was labeled “> 0.5 per km density”. These green and red polygon boundary lines clearly encircle the majority of my black polygons. So, I think I am on the right track. But I really have no idea how to progress from my numerous purple and black polygons to a solid green or solid red polygon created by the other analyst. I do not know whether he used QGIS or ArcGIS or R or some other software. He may have used a smoothing procedure, but I am unfamiliar with that.

Here are the menu procedures I used to create the purple and black polygons with QGIS:

a. Import Shape File

     1. Layer > Add Layer > Add Vector Layer > fake_points_oahu_utm.shp

b. Heatmap

     1. Processing Toolbox > Interpolation > Heatmap (Kernel Density Estimation)
     2. Use 1000 m radius
     3. I manually set x and y pixel size to 1000 meters: 86 rows and 86 columns
     4. Use the default quartic kernel

c. Contours Polygons

     1. Processing Toolbox -> GDAL > Raster Extraction > Contour Polygon
     2. Interval between contour lines: 0.5

d. Base map

     1. Web > QuickMapServices > OSM > OSM Standard

How can I obtain solid polygons similar to those encompassed by the hand-drawn green or red boundaries from my large number of black polygons (or black and purple polygons)?

I also tried just creating contour lines in increments of 0.5 but a large number of scattered contours resulted. Perhaps I need to dissolve the black polygons and apply some sort of smoothing procedure, but I really have no idea how to do that.