the way in which an open world is designed from the ground up (e.g. as an activity-focused world or an exploration-centric one with little to no handholding)
Do you mean open world games that use markers are designed from the beginning to be focused on activities, a to-do-list, rather than exploration? Or is that just a personal impression?
I'm curious because it never seemed that way to me.
Skyrim for example, if you disable markers, will still have the NPCs that give a quest tell you more or less where to go, at least in the region of which city, or you hear people in some town talking about rumours, about the college in Winterhold etc etc, and since it's a chartered region with villages, castles and roads, it's possible to simply follow along a way until the next crossroads, check the roadsigns and decide if you check out what you heard about Riften this way or Solitude that way...
The landscape encourages exploration, at least in my case I always decided to go look at that waterfall, see what's over that hill, or simply follow a river hunting mudcrabs, suddenly discovering some beautiful hot springs nobody ever told me about...
It may be possible that games that intentionally don't use map markers (I haven't played Elden Ring) are designed in a way that you don't feel lost because they take that into account, but I still find it hard to believe that was the case with older games, so I'm skeptical of "old school" glorification when some tools simply weren't available or widespread a few decades ago.
I'd say it depends a lot on the setting we're in. In a culturally developed and educated surrounding like the world of AC: Odyssey I'd find it outright immersion breaking as a roleplayer if my ship's captain had no idea how to reach the Piraeus, or which way to find which island, or if nobody in the area of greater Athens had a map that shows me where to find this or that temple.
If I'm playing a prisoner who escapes from a penal colony somewhere on an unchartered island, it's a different matter.
I just get very careful when people discuss maps vs natural exploration like a religious war, especially when words like "old-school" and "hardcore" vs "handholding" are thrown around, because we've all read discussions where people used these terms to distinguish themselves as the "true" gamers as opposed to the "casual" ones.
Even the same game can be played in many different styles, and I remember the times where people bought walkthroughs to play a game or later searched for them on the internet, so they probably weren't all happy natural explorers before quest markers were invented.
So different game designs should depend on different purposes and fit the general setting and tone of the game, and I stand by my point that role-playing is not more encouraged or rewarded through lack of quest markers, and that open world games with map markers can be and are far more than activity playgrounds to check off your to-do lists.
The context matters more for role-playing (i.e. very simplified: Give me a map if I'm in a civilized world with paved roads and letters and possibly magic, don't give me one if I just escaped from a prison colony, stranded on an alien planet or am a cave troll in Antarctica) at least to me.