What you linked is very different. It’s something you write down but are expected to still remember later. If this helps you with your grocery list, then yes this is good, but if instead of actually using your memory you look at the list, that’s what’s bad. Writing itself is very good, it’s not having to recall it that’s not.

In a test at school for example, handwritten notes does help memory, since you’re still expected to use your brain later to remember it, as opposed to reading the notes.

Note that while I say it’s “bad”, it’s really just one factor among many. Just like everyone knows sugar is bad yet everyone consumes it to some extent. But the more of those “bad” things you avoid, the more likely you are to suffer from memory issues later.