There have been, admittedly, no studies on specific digital tools and their impact on the working memory, though at the same time, even the benefit of actively training working memory is inconclusive at best[0].
In general, I am doubtful over any statement that general use of modern technology could lead to a short-term memory impairement.
Plato (400 BC)
There’s always tension in Plato as to what was his opinion and what was Socrates’. Furthermore many characters in his dialogues are explicitly meant to be wrong in their opinions. Just reading a Plato quote as evidence of Plato’s actual opinion is a route to confusion.
This idea as communicated in Phaedrus, by Socrates, was certainly Socrates’ opinion: Socrates never wrote anything down.
Digital tools mostly seem help me with long-term memory and doesn't do a thing for the working memory exercise.
I can look up a phone number or have a calendar on what I'm doing next Wednesday, but the working memory of "what am I doing right now" hasn't gone digital yet. Navigation has vaguely the same, because it's more long form memory rather than the hot list in my brain (maybe "what gear am I in?" on a manual car? doubtful).
Of all the day to day activities I do, cooking is one of those things where I've really felt like my working memory is working hard & despite quite a few tools like timers or automatic cookers, the way the kitchen is organized with closed drawers is a most-recent working memory exercise like those face-down card games.
If anything digital tools greatly improve my memory by allowing me to offload things.
I play video games, I play instruments, I write programs, and I have to imagine that all of it helps, but I haven't tried "brain training" or used tools marketed as improving working memory. I'm not even really sure what's on offer in that space, so if you've found some I'm curious to know about them.
I can’t think of any better test than trial by fire. Kind of like learning languages. Study all you want, theory won’t save you when it comes to practical application. :)
When it comes to programming, becoming familiar with your tools and learning to offload stuff to paper far exceeds anything else. If you know something well, you need less working memory to do it.
Jim Keller raised this point in one of his Lex Fridman interviews. They're some of the more worthwhile ones to listen to IMO.
The diagnosis of Marilu Henner’s recall ability as Hyperthymesia (per her Wikipedia article) seems to confirm this is a mutation compared to typical memory formation.
That aside, long term memory is indeed distinct from working memory. Long term memory is formed from your working memory, but the memories are stored separately.