Here is a weird one.

I found a printed flashcard that lists the simplified and traditional characters for the English word "what?" (pinyin: shen2) as: 什 (simplified) and 甚 (traditional). Weirdly, it is the simplified version that corresponds to Heisig & Richardson's "what?" / shen2 as RTH #743. The character that my flashcard shows as the traditional version for "what?" corresponds with Heisig & Richardson's RTH #1291, pronounced shen4 with a keyword of "tremendously".

On Rosetta Stone set to Traditional characters, the word for "what?" is at all times given as: 甚麼 (shen2 me5) and "why?" or "how come?" as 為甚麼 (wei2 shen4 me5). Google Translate gives both 為甚麼 and 為什麼 as possible traditional hanzi translations for "why?", but lists only 什麼 for "what?"

Can anyone help me sort this out? To what extent are 什 & 甚 interchangeable?

According to my wife (a native speaker from Taiwan), these two characters are completely interchangeable. 甚 is a variant form of 什, so they can both be used in the context of "what" and "why".
甚 may have been the preferred form a few generations ago, but nowadays 什 seems to be more frequently used in traditional characters.

Thanks, Rubrick. That is very helpful & makes sense. It seems a handful of simplifications may have made their way into the traditional lexicon.

I have a feeling that the same situation is true for these hanzi:
RTH #621 (台 / tai2 / platform) which my outside cards call the simplified version of 臺.
RTH #50 (只 / zhi3 / only) which my outside cards call the simplified version of 祇.

Yes, you're absolutely right. Although 祇 is really, really old (but apparently still used by some old people)