Joe,
I attempted to put together what I thought you were saying more or less. So far, I haven't got it to work. I put the error below the code. I thought I'd try deleting the feature classes in the dataset first, then copy the shapefiles into that dataset.
import arcpy
from arcpy import env
import os
shps = r'pathto\Test\shapefiles'
dataset = r'pathto\TestFGDB.gdb\dFIRM_2019_Effective'
shpList = arcpy.ListFeatureClasses()
fcList = arcpy.ListFeatureClasses()
for fc in fcList:
arcpy.Delete_management(dataset, "FEATURECLASS")
arcpy.CopyFeatures_management(shpList, dataset)
print("done")
line 15, in <module>
for fc in fcList:
TypeError: 'NoneType' object is not iterable