Blender stores your recent files in a txt file, [1][2] located in your OS' .config/blender/version/config/
folder. So once you save it, you just manually prepend the filepath to the beginning of that txt file and reread it in.
import bpy
from pathlib import Path
# recent files stored in a text file in your .config folder
# these paths I included below will probably need to be properly escaped, since windows is weird
recent_files = "C:\Users\<Userbane>\AppData\Roaming\Blender\\Users\\<Userbane>\\AppData\\Roaming\\Blender Foundation\Blender\<yourFoundation\\Blender\\<your-blender-version>\config\recentversion>\\config\\recent-files.txt"
save_path = Path('C:\Desktop\my_blend\\Desktop\\my_blend.blend')
bpy.ops.wm.save_mainfile(filepath=save_path)
# add the blendfile path to the recent-files.txt
with open(recent_files, 'r+') as f:
contents = f.read()
f.seek(0,0) # go to beginning of file
if save_path.is_file():
newfile = save_path.resolve().rstrip('\n\r') + "\n" + contents
f.write(newfile)
else:
print("File did not save correctly.")
# reread file history
bpy.ops.wm.read_history()