The distribution of digits is 'highly imbalanced' because that's what random distributions look like. I'll randomly select the digits 0-9 for 10,000 times and show the distribution, then do the same with the first 10,000 digits of pi, then do the random distribution again:

  >>> import random
  >>> from collections import Counter
  >>> ctr = Counter(random.choice(range(10)) for i in range(10_000))
  >>> for digit, count in ctr.most_common():
  ...   print(f"{digit}: {count}")
  ...
  2: 1039
  4: 1035
  0: 1031
  7: 1022
  3: 1008
  6: 998
  1: 976
  5: 973
  9: 963
  8: 955
  >>> pi_ctr = Counter(open("1-10000.txt").read().rstrip())
  >>> for digit, count in pi_ctr.most_common():
  ...   print(f"{digit}: {count}")
  ...
  5: 1046
  1: 1026
  2: 1021
  6: 1021
  9: 1014
  4: 1012
  3: 974
  7: 970
  0: 968
  8: 948
  >>> ctr = Counter(random.choice(range(10)) for i in range(10_000))
  >>> for digit, count in ctr.most_common(): print(f"{digit}: {count}")
  ...
  8: 1060
  2: 1048
  0: 1034
  4: 1026
  5: 1025
  3: 979
  7: 977
  6: 960
  1: 956
  9: 935

You can see that the distribution of pi's first 10,000 digits is what one should expect for a random distribution. If your method requires a 50/50 distribution then it cannot be used for this purpose.

Also, you are thinking about it wrong. The first 10,000 digits of pi are perfectly predictable.

Because "somewhat predictable" doesn't mean "non-random". In fact, almost all prefixes of algorithmically random bit sequences are somewhat predictable with an appropriate definition of "somewhat", because you can find and exploit an accidental bias from taking the prefix and any such bias translates to some predictability.

(Another possibility is that, since pi itself is not really algorithmically random, the classifier was somehow able to learn how to partially compute pi! That's another pitfall you need to avoid even when you have a good understanding of information theory and statistics...)