This was intentional, because System Settings' Icon View is more akin to a grid of buttons (which always perform an action on single-click) than a file view where there are multiple actions you can perform on a selected icon (which is the entire point of double-click).

See Bug 377309.

Even if intentional, from a users point of view, this is totally inconsistent.
When I use konqi or systemsettings, I do not differentiate. You know, muscle memory, therefore double click is my natural action.
And an icon view is not a set of buttons. A PushButton has a different look and feel. When I recogize a button by its look, it would be understandable, but here it is not.

The behavior is totally consistent, but it's consistent with the actual reason for double-click to exist.

The entire reason for double-click to exist is because certain things have a state where they can be selected, and in that state, you can perform non-opening actions on them. For such items, some people find it useful to enter that selected state with one click, so they can perform actions on the item without having to use a context menu. This is literally the only reason for anything to ever be double-clickable.

Files and folders can be double-clickable because they have a state where they can be selected, in which you can perform rename actions, copy actions, delete actions, etc. Therefore it makes sense to offer an option for them to open on a double-click, because some people prefer for the single-click action to be "select this item" not "open this item."

These icons here in System Settings have no selection state in which it is possible to perform any actions. You can't copy them. You can't email them to someone else. You can't delete them. The only thing you can do with them is open them. You can't rename them. The only thing you can do with them is open them. There is only one action they perform.

What do you call a clickable UI element has exactly one action and only one action that it can perform when interacted with? A button. And buttons never have to be double-clicked to make them perform their action. They always perform their action on the first click, even when you use the systemwide double-click setting.

System Settings' icon view is a grid of buttons. The buttons may not look like buttons, but that's not unusual; a ToolButton is a button that doesn't look like a button. We use non-buttonlike buttons all over the place throughout KDE software. This is personally not my favorite thing in the world, and if I had my way, all buttons would have a visibly buttonlike appearance.

Alas, this is not the majority view, so I accept it. And because of that, System Settings' Icon View is a grid of non-buttonlike buttons. So they open their KCMs on a single-click, just like all other buttons to.

I absolutely understand the reasoning.
Although I still dislike the continuous change in behavior (and arrangement) of things in KDE which I got used to the last 10, 20 or so years.

That's a reasonable complaint.

However, it's awfully hard to fix bugs when people complain that they got used to the bugs over time! Either we can fix bugs, or we can't. We also get complaints every time anything visual changes, or anytime we change any default settings, but it's not really reasonable to expect the whole system to be frozen in amber forever.

However being annoyed when something changes (even if it was for an ostensibly good reason) is still reasonable, so you might be interested in participating in this discussion: https://invent.kde.org/plasma/plasma-workspace/-/issues/11