> But why only using 2 digits for log2(10) estimation?

Because the difference between 3 and 3.3 is 10%, and the difference between 3.3 and exact log2(10) is only 1%. Yes, we can use more digits, but the effect of any additional digit is decreased in geometric progression.

If use simple and fast formula that avoids integer multiplication overflow "digits + digits // d", the effect of additional precision is virtually vanished.

>>> PyLong_SHIFT, _PyLong_DECIMAL_SHIFT = 15, 4
>>> (3 * _PyLong_DECIMAL_SHIFT) // (1 * PyLong_SHIFT - 3 * _PyLong_DECIMAL_SHIFT)
4
>>> (33 * _PyLong_DECIMAL_SHIFT) // (10 * PyLong_SHIFT - 33 * _PyLong_DECIMAL_SHIFT)
7
>>> (33219 * _PyLong_DECIMAL_SHIFT) // (10000 * PyLong_SHIFT - 33219 * _PyLong_DECIMAL_SHIFT)
7

>>> PyLong_SHIFT, _PyLong_DECIMAL_SHIFT = 30, 9
>>> (3 * _PyLong_DECIMAL_SHIFT) // (1 * PyLong_SHIFT - 3 * _PyLong_DECIMAL_SHIFT)
9
>>> (33 * _PyLong_DECIMAL_SHIFT) // (10 * PyLong_SHIFT - 33 * _PyLong_DECIMAL_SHIFT)
99
>>> (332 * _PyLong_DECIMAL_SHIFT) // (100 * PyLong_SHIFT - 332 * _PyLong_DECIMAL_SHIFT)
249
>>> (3321 * _PyLong_DECIMAL_SHIFT) // (1000 * PyLong_SHIFT - 3321 * _PyLong_DECIMAL_SHIFT)
269
>>> (33219 * _PyLong_DECIMAL_SHIFT) // (10000 * PyLong_SHIFT - 33219 * _PyLong_DECIMAL_SHIFT)
290
>>> (332192 * _PyLong_DECIMAL_SHIFT) // (100000 * PyLong_SHIFT - 332192 * _PyLong_DECIMAL_SHIFT)
291
>>> (332192809 * _PyLong_DECIMAL_SHIFT) // (100000000 * PyLong_SHIFT - 332192809 * _PyLong_DECIMAL_SHIFT)
291

The best approximation with minimal denominator is 485/146.

>>> PyLong_SHIFT, _PyLong_DECIMAL_SHIFT = 15, 4
>>> (485 * _PyLong_DECIMAL_SHIFT) // (146 * PyLong_SHIFT - 485 * _PyLong_DECIMAL_SHIFT)
7
>>> PyLong_SHIFT, _PyLong_DECIMAL_SHIFT = 30, 9
>>> (485 * _PyLong_DECIMAL_SHIFT) // (146 * PyLong_SHIFT - 485 * _PyLong_DECIMAL_SHIFT)
291