start_time = django_filters.TimeFilter(lookup_expr='gte', field_name='created_at__hour', input_formats="%H")
end_time = django_filters.TimeFilter(lookup_expr='lte', field_name='created_at__hour', input_formats="%H")
Input: start_time = 10
Result: { "start_time": [ "Enter a valid time." ] }
Since you filter on the __hour lookup, these are integers, so you filter with:
start_time = django_filters.NumberFilter(lookup_expr='gte', field_name='created_at__hour')
end_time = django_filters.NumberFilter(lookup_expr='lte', field_name='created_at__hour')