Read the Markdown spec where it says the > denotes a blockquote. There isn’t room to overload it without breaking that into something not backwards compatible (such as CommonmsMark which will follow the spec & render a blockquote—which, according to the HTML spec, must be text quoting a source). Just because some of the bigger players—namely the proprietary forks, Obsidian & MS GitHub—doesn’t mean it’s not breaking with the original spec. Go ahead & do it, but don’t lie & say it is Markdown or Markdown-compatible. Instead these entities try to push & sway everyone to adopt their syntax rather than working with say CommonMark with RFCs.

CommonMark has the ::: block syntax, but folks using this are relying on stringly-typed, not-well-defined options when they do ::: note as it just becomes a CSS class where anyone could style it.

As callouts are such an everpresent construct in technical writing, documentation, & so on, what you need is first-class support. Docbook as an output has first-class support, but sadly W3 shot down the last attempt at an element proposal (but can be properly by manually constructed with role=note & aria-labelledby). reStructuredText & AsciiDoc are both lightweight markup syntaxes that support first-class callouts & other elements (definition lists, summary/details, figures, etc.) as well as having first-class metadata (like basically every other creative work format for images, audio, documents).

All of this is to say what Microsoft is doing is no longer Markdown & only they hold the keys to the spec (you can complain in their forums, but you can’t submit an RFC or pull request). But also, Markdown / CommonMark are honestly ill-suited for the task of technical writing since it doesn’t support basic features for that task (embedding HTML defeats the purpose & portability)—and instead we have a lot of ad-hoc hacks & bad HTML output due to choosing the wrong tool for the job.