Correct. Stunned characters do not have powers and keywords.
502.1
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Triggered powers are identified by the words “at the start of,” “when,” or “whenever.” Triggered powers wait
for their trigger events to occur, at which point they trigger. Triggered
powers generate triggered effects on the chain.
502.4
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Triggered powers that trigger off an object becoming
stunned, leaving play, or causing breakthrough look back to the game state at
the moment right before the object became stunned, left play, or caused
breakthrough. This information is only used to determine whether they could have triggered off that
event and whether they did.
The effects you mentioned are triggered effects that trigger off of a charcater becoming stunned, so 502.4 explains how to resolve these effects. Let's use the Secret Society Scarecrow from DJL as an example. He gains a +1/+1 counter whenever he stuns a character. Lets say he is in combat with another 5-drop and becomes stunned. Scarecrow has a stun triggered power so you look bak to right before both characters were stunned to see what happens. Scarecrow gains the +1/+1 counter even if he is stunned at the same time that he stuns another character.
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