Automate QGIS v.kernel.rast across multiple nested folders with Python

I'm using QGIS 3.40.8 and need to automate kernel density calculations across a nested folder structure. I don't know Python - the code below was created by an LLM based on my QGIS log output from running v.kernel.rast manually in the GUI.

Current working code (single folder):

import processing
import os
from qgis.core import QgsRasterLayer

# === Inputs ===
point_layer = 'main_folder/manchester/2018/01/poi.shp'
reference_raster = 'main_folder/manchester/2018/01/lc.tif'
output_dir = 'main_folder/manchester/2018/01/'

# === Bandwidths to test ===
bandwidths = [50, 100, 150, 200]

# === Extract parameters from reference raster ===
print("Extracting parameters from reference raster...")
ref_layer = QgsRasterLayer(reference_raster, "reference")

if not ref_layer.isValid():
    print(f"ERROR: Could not load reference raster: {reference_raster}")
    exit()

# Get extent
extent = ref_layer.extent()
region_extent = f"{extent.xMinimum()},{extent.xMaximum()},{extent.yMinimum()},{extent.yMaximum()} [EPSG:{ref_layer.crs().postgisSrid()}]"

# Get pixel size
pixel_size = ref_layer.rasterUnitsPerPixelX()

print(f"Extracted region extent: {region_extent}")
print(f"Extracted pixel size: {pixel_size}")

# === Kernel density loop ===
for radius in bandwidths:
    output_path = os.path.join(output_dir, f'kernel_bw_{radius}.tif')
    print(f"Processing bandwidth: {radius}...")
    processing.run("grass7:v.kernel.rast", {
        'input': point_layer,
        'radius': radius,
        'kernel': 5,  # Gaussian
        'multiplier': 1,
        'output': output_path,
        'GRASS_REGION_PARAMETER': region_extent,
        'GRASS_REGION_CELLSIZE_PARAMETER': pixel_size,
        'GRASS_RASTER_FORMAT_OPT': 'TFW=YES,COMPRESS=LZW',
        'GRASS_RASTER_FORMAT_META': ''
    })

print("All kernel rasters created.")

Folder structure:

main_folder/
├── city (e.g., rome)/
│   ├── year (e.g., 2018)/
│   │   ├── month (e.g., 11)/
│   │   │   ├── poi.shp
│   │   │   └── lc.tif
│   │   └── 04/
│   │       ├── poi.shp
│   │       └── lc.tif
│   └── 2019/
│       └── 11/
│           ├── poi.shp
│           └── lc.tif
└── london/
    └── 2021/
        └── 03/
            ├── poi.shp
            └── lc.tif

What I need:

• Loop through all monthly folders following the pattern: main_folder/city/year/month/
• Skip folders that don't contain poi.shp
• Run kernel density analysis for each valid monthly folder
• Save output rasters in the same monthly folder where poi.shp is located
• Files are consistently named: poi.shp (points) and lc.tif (reference raster)

How can I modify this code to automatically iterate through the entire nested folder structure?