this is correct but i think op is asking the wrong question.

at least from a mathematical perspective, the claim that pi contains any finite string is only a half-baked version of the conjecture with that implication. the property tied to this is the normality of pi which is actually about whether the digits present in pi are uniformly distributed or not.

from this angle, the given example only shows that a base 2 string contains no digits greater than 1 but the question of whether the 1s and 0s present are uniformly distributed remains unanswered. if they are uniformly distributed (which is unknown) the implication does follow that every possible finite string containing only 1s and 0s is contained within, even if interpreted as a base 10 string while still base 2. base 3 pi would similarly contain every possible finite string containing only the digits 0-2, even when interpreted in base 10 etc. if it is true in any one base it is true in all bases for their corresponding digits

speaking and typing are not comparable whatsoever

bro what are you on about. do you really think there were no equivalent problems back then weve since solved? i cant examplify because i was not alive at that time and im not read up enough but to me its obvious every time period will have their own challenges, and stop putting words in ppls mouths lol