Python Script for Zonal Statistics As Table results empty Table

I downloaded your files and it worked just fine. Pretty sure your issue is that your files are ADF (Esri Grid files, not a TIF) so simply change this line

raster_list = arcpy.ListRasters("*.tif")

to this

raster_list = arcpy.ListRasters("*")

And it should work. I had no problem with it working.

The script worked fine when I removed the "NODATA" value I was passing to the ignore_nodata parameter and simply put the double quotation instead. This switches the functionality from ignoring all zones that contain NODATA values to the default behavior of excluding NODATA values from the calculations of a zone's statistics and not skipping zones that contain NODATA values.

import os
import arcpy
from arcpy import env
from arcpy.sa import *

arcpy.env.overwriteOutput = True
arcpy.CheckOutExtension('Spatial')

arcpy.env.workspace = "D:/Data/Hydro/"

raster_list = arcpy.ListRasters("*.tif")
lisTable = arcpy.ListTables()

zone = "D:/Data/Catch.shp"

# Loop through each file and perform the zonal statistics processing
for raster in raster_list:
    raster_name = os.path.basename(raster).rstrip(os.path.splitext(raster)[1])
    outTable = raster_name + ".dbf"
    arcpy.gp.ZonalStatisticsAsTable(zone, "NAME", raster, outTable, "", "MEAN_STD")