You were right about the Memories! I found that "Memory updated" thing at one point, so that would explain the Motivation Letter examples.

But...

"Memory is disabled. ChatGPT won't use or create memories."

and nothing is stored there. Weird.

Still, the on-the-fly translation remains a mystery

Thank you for this hint. I checked both the app and the website and I don't have this feature. Or maybe I do have it in the chat but not yet visible in Settings...? I will keep an eye on this.