This is the issue:
6-03 06:15:39.043 13463 13580 I python : File "/home/nexgen/Desktop/Work_Stuff/pymongo_test/.buildozer/android/platform/build-armeabi-v7a/build/python-installs/pymongo_test_2/dns/resolver.py", line 782, in read_resolv_conf
06-03 06:15:39.053 13463 13580 I python : FileNotFoundError: [Errno 2] No such file or directory: '/etc/resolv.conf'
The code is POSIX specific, so not portable.
It is looking for a Linux OS system file that does not exist on the Android OS. And it did exist it would not be readable.
Clearly this is about dns name resolution.
I don't know how to use the default Android nameserver, I'd guess it is in the developer docs and would be accessed via pyjnius.
But before spending much time on that, check if pymongo needs a resolver for some internal magic of its own, which might complicate the task.