How to put GeoJSON coordinates to TIFF?

The polygon seems to be a north-up oriented rectangle so you can simply assign the upper-left and lower-right coordinates into the image.

With Python you can then use https://gdal.org/python/osgeo.gdal-module.html#Translate and use the options as documented in https://gdal.org/python/osgeo.gdal-module.html#TranslateOptions

You can test the conversion with the gdal_translate utility https://gdal.org/programs/gdal_translate.html#gdal-translate

Usage:

gdal_translate -of GTiff -co tiled=yes -ullr 66.87480926513672 48.119751843350834 66.89043045043945 48.111213657240576 input.png output.tif

The coordinate system of the polygon is probably EPSG:4326 and you can assign that with -a_srs epsg:4326. However, the png that you have may actually use some other crs like EPSG:3857. In this case some additional steps are needed.

In Georeferencing raster using GDAL and Python?

# Specify raster location through geotransform array
# (uperleftx, scalex, skewx, uperlefty, skewy, scaley)
# Scale = size of one pixel in units of raster projection
# this example below assumes 100x100
gt = [-7916400, 100, 0, 5210940, 0, -100]

You can use the script of Ian Turton in Convert GeoJSON object to bounding box using Python 3.6, the library geojson-bbox and others.

import gbbox #geojson-bbox
pol = {"type":"FeatureCollection",
"features":[{"type":"Feature","properties":{},"geometry":{"type":"Polygon","coordinates":
[[[66.87480926513672,48.111213657240576],
[66.89043045043945,48.111213657240576],
[66.89043045043945,48.119751843350834],
[66.87480926513672,48.119751843350834],
[66.87480926513672,48.111213657240576]
]]}}]}
min_x, min_y, max_x, max_y =  gbbox.GeoJSON(pol).bbox()
print( min_x, min_y, max_x, max_y)
66.87480926513672 48.111213657240576 66.89043045043945 48.119751843350834

And you get uperleftx (min_x), and uperlefty (max_y). Assuming 100x100 as in Georeferencing raster using GDAL and Python?

 gt = [66.87480926513672 , 100, 0, 48.119751843350834, 0, -100]

But in reality you need the size of the raster (width, height) to compute the real size of the pixel