The double-hyphen is by no means "old school": it's a kludge for twentieth-century systems like typewriters and word processors that did not have em dashes or an easy way to insert them. The very names "em dash" and "en dash" should illustrate their age: they go back to the fifteenth century, and "em" and "en" were standard printing widths in moveable type. People who write CSS still recognize em as a width.

The idea that a double-hyphen is "old school" is on par with the false notion that double-spacing between sentences is a product of the typewriter; one need only look at a typeset book from before the twentieth century to see the truth, or look at a decent image of the Declaration of Independence or other hand-written document from prior centuries to see the extra space left between sentences.

Many of the changes we see in written English style are the product of ignorance of the past beyond two generations or so. Avoiding em-dashes to keep up with the latest anti-AI fad is just reacting mindlessly to the stimulus of popular ignorance instead of deliberately situating one's style in the history of writing conventions.