Looking for best way to write math notes using Latex and markdown

I am currently looking for a way to take math note using latex and markdown.
The features what I want are

1. Real Time Preview (so I don’t need to save it to preview)
2. Can define macros
3. Can use packages of Latex such as amsmath

Since Latex itself is compile-language, most of the options are not real time. Therefore, I think markdown with Latex can be a solution. However, I can’t find an option that supports all three of them. I tried…

1. VScode with markdown+math extension (Use Katex, meaning 3 is not satisfied)
2. Atom with markdown preview plus extension (seems 3 is not satisfied)
3. [edit] I tried Overleaf with autocompile with fast option. (the compile time is too slow. meaning it is essentially not a real time preview)

[edit]
The real time preview I want is something like the following.

Could you please help for this problem?

Thank you