This "figuring out" is just going to come from stuff it was trained on - people discussing why LLMs fail at certain things, and those people (training samples) not always being correct about it!
The "How many R's in "strawberry, counting words in a sentence, reversing strings. I process text as tokens, not characters, so these are surprisingly error-prone" explanation sounds plausible, but I don't think it it correct.
Any model I've ever tried that failed on things like "R's in strawberry" was quite capable of reliably returning the letter sequence of the word, so the mapping of tokens back to letters is not the issue, as should also be obvious by ability of models to do things like mapping between ASCII and Base64 (6 bits/char => 2 letters encode 3 chars). This is just sequence to sequence prediction, which is something LLMs excel at - their core competency!
I think the actual reason for failures at these types of counting and reversing tasks is twofold:
1) These algorithmic type tasks require a step-by-step decomposition and variable amount of compute, so are not amenable to direct response from an LLM (fixed ~100 layers of compute). Asking it to plan and complete the task in step-by-step fashion (where for example it can now take advantage of it's ability to generate the letter sequence before reversing it, or counting it) is going to be much more successful. A thinking model may do this automatically without needing to be told do it.
2) These types of task, requiring accurate reference and sequencing through positions in its context, are just not natural tasks for an LLM, and it is probably not doing them (without specific prompting) in the way you imagine. Say you are asking it to reverse the letter sequence of a 10 letter word, and it has somehow managed to generate letter # 10, the last letter of the word, and now needs to copy letter #9 to the output. It will presumably have learnt that 10-1 is 9, but how to use that to access the appropriate position in context (or worse yet if you didn't ask it to go step by step and first generate the letter sequence, so the sequence doesn't even exist in context!)? The letter sequence may have quotes and/or commas or spaces in it, and altogether starts at a given offset in the context, so it's far more difficult than just copying token at context position #9 ! It's probably not even actually using context positions to do this, at least not in this way. You can make tasks like this much easier for the model by telling it exactly how to perform it, generating step-by-step intermediate outputs to track it's progress etc.
BTW, note that the model itself has no knowledge of, or insight into, the tokenization scheme that is being used with it, other than what is available on the web, or that it might have been trained to know. In fact, if you ask a strong model how it could even in theory figure out (by experimentation) it's own tokenization scheme, it will realize this is next to impossible. The best hope might be some sort of statistical analysis of it's own output, hoping to take advantage of the fact that it is generating sub-word token probabilities, not word probabilities. Sonet 4.6's conclusion was "Without logprob access, the model almost certainly cannot recover its exact tokenization scheme through introspection or behavioral self-probing alone".