It works with double-click only.

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We need to check whether it respect list and tree VS Code settings.
We need to check whether it respect
listandtreeVS Code settings.
I do not understand this comment.
I meant whether this view respects following settings in VS Code:

I set the open mode preference to doubleClick, and the files still open with a single click from the call stack view.

The open mode preference is ignored by the debug view.
Note that some trees and lists might choose to ignore this setting if it is not applicable.

VS Code reacts to double click as well. The difference is that single click preview, i.e. focus is not transferred and editors are not pinned (previewed). Double click or enter transfers cursor and pin the editor.