Addendum, after looking further into it.
It seems even the supplied conditions in the “Activation Group” when you download the preset do not seem to work. Blender is setup in there by default and when I select text in a Blender it is replaced by a “c”. The Key overlay of CleanShot X shows the “cmd” key as well. On a side note: I cannot use the “drag to select capture area” of CleanShot X, since after dragging the “text selection did change” trigger activates and (probably) sends a “cmd-c” which exits the screen recording overlay.
Something seems odd with this trigger. Tools like PopClip do not have this issue, maybe they get the selected text in a different way.
The issue with CleanShot X, or in general with “Text Selection Did change” trigger stealing focus/sending key commands is also mentioned in another issue: BTT Text Selection steals focus?