zlib successfully decompresses data that it has compressed previously:

>>> data = b'data'
>>> import zlib
>>> compressed = zlib.compress(data)
>>> import base64
>>> original_data = base64.b64encode(compressed).decode()
>>> zlib.decompress(base64.b64decode(original_data))
b'data'

zlib fails to decompress (with the default settings) gzip data:

>>> import gzip
>>> gzipped_data = base64.b64encode(gzip.compress(data)).decode()
>>> gzipped_data != original_data
True
>>> print(zlib.decompress(base64.b64decode(gzipped_data)))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
zlib.error: Error -3 while decompressing data: incorrect header check
>>> gzip.decompress(base64.b64decode(gzipped_data))
b'data'

I don't really understand what issue you may be encountering, it should operate as normal. Always be careful when using exec() for things like this as it is used a lot by threat actors for running binaries.

import zlib, base64
a = zlib.decompress(base64.b64decode('eF7zSM3JyVcIzy/KSVFU8FTPVcjPUwguSUzO9i9LLUrLyS9XBADJNQvD'))
print(a)

Output: b"Hello World! I'm on StackOverflow!"

This is the problem, I suspect:

byte[] compressed = System.Text.Encoding.UTF8.GetBytes(childNodes.Item(i).InnerText.Trim());

You said that your data is compressed and then base64-encoded... but your code doesn't use base64 anywhere, which is a massive warning sign. I suspect you want:

string text = childNodes.Item(i).InnerText.Trim();
byte[] compressed = Convert.FromBase64String(text);

If that doesn't work, you should check each step of the transformation - you should have the same data during encoding and decoding, just in the reverse order. See my blog post about diagnosing reversible data transformations for more details - but hopefully the change above will fix it anyway.

You first need to decode the base64, then zlib decompress:

import zlib, base64
decompressed_data = zlib.decompress(base64.b64decode(data))

Looking at your data, it appears to be UTF-8 encoded XML, so we're almost there:

xml = decompressed_data.decode("utf-8")