To what keys do chords like C6, C6/9 , Gm7b5 or dominant 7 sharp ninth chords, suspended chords, power chords, belong to?
Note: I don't specifically mean C6, I'm more focused on the type of chord and not the chord itself.
For that matter, apart from the minor, major, seventh and diminished chords in every key, how do I determine in which key do the other chords (like 6th chords, ninth chords, dominant 9, dominant minor 9) belong to?
Edit: ( I wasn't clear earlier)
What I meant was, for example when we Google "chords in C major" we get the I-vii° chords of C major and the added 7th chords. This goes for any key that I Google. But what about the fancier chords like C6/9, dominant 7sharp 9, and all those jazz chords? I've never seen these chords pop up when someone Googles for chords in a key. So I was wondering to what chords these keys belong to and how one goes about determining that.
Edit edit: to be more clear, I tried to put many doubts into one question and hence the confusion. I'd rather just split the entire question into subdivisions.
1) a dominant 7 sharp 9 chord belongs to which key? Eg: Gdom7#9
2) a suspended chord belongs to which key?
3) a power chord belongs to which key? And how do you determine it?
4) a ninth chord or 6/9 chord belongs to which key? And how do you determine it?