The dirty little secret is...there is no "true markdown". There are multiple different implementations of markdown that have been created by different people at different times, all vaguely based on the original not-very-robust definition created by John Gruber with assistance from Aaron Swartz in 2005. But their definition never mentioned superscript at all.

Because of how unrobust it is, in 2014, some people got together to define a robust specification and called it CommonMark. But again, this does not mention superscript.

The closest you'll find to an "official" specification for the extra bits of markdown that aren't in the CommonMark spec is probably here. But this is really more attempting to describe extended markdown as it is used on the web at large already. In addition to super- and sub-script, it also deals with tables (which work the same way Reddit does them) and fenced code blocks (the triple backtick method, which Reddit does not support—instead supporting only code blocks via four spaces). Though both fenced and indented code blocks are actually in the CommonMark spec.

Reddit, obviously, is one site that famously implements markdown, and has done for a very long time. On Reddit, superscript is done with a caret before the superscript text, and whitespace after it. Unless you use brackets, in which case the superscript lasts until the closing bracket. e.g. normal^superscript text would make "superscript" superscript, but nothing else. But normal ^(superscript text) would make "superscript text" superscript. But then there's a second caveat, which is that Reddit supports double (and triple, etc.) superscript. But in these cases, brackets do not work. They unintuitively completely break things.

Lemmy also uses markdown. The Lemmy specification for how to use markdown is located here. You'll note that it supports both superscript and subscript, which Reddit does not. It does both of these according to the method explained in the "markdown guide". Though there are a few issues with inconsistent parsing of the markdown on lemmy-ui (the default web front-end) and some apps (including Jerboa, the 1st-party app).

The big advantage of the markdown guide method is that it is most similar to how other markdown works. You don't implicitly close italics on a word with just one asterisk; you need two asterisks—one to open italics, one to close them. Likewise, bold with double asterisks. By using a character to both open and close your super/sub-script, you are making a much clearer and more deliberate intention about what you want, and allowing people to learn things more intuitively, because it all works the same way as each other.