I don’t know how difficult this would be to implement, but a feature like this would be a godsend:
Pick one note, and have Scaler give you what chords it could belong to.
For example, a C note could be the root of a C maj/ min/ etc… chord, the 5th of an F chord, the 7th of a Ddom7, the 11th of Gmin11 chord, etc…
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That’s just staying in the key of C. The OP is also wanting to add any chord C could be a part of in any key. Not a useful list and Scaler already does suggestions in the Modulations section. It’s all there.
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Sorry, I’m not used to thinking of say a Gmin add C, etc. as an inversion of C per se.
I think this
part is largely covered by this Scaler feature…
Pick a scale with the note that you want to have chord variations for, in this case I chose C Major to get everything related to C. Section B will automatically show the base chords for the scale. There you click on “VARIATIONS”
…then choose “TONIC” (note C in this case)…
…and this gives you a long list of chord variations based on the C major chord. If you want C minor then chose the C minor scale at the beginning.
And this list is very long, wider than the screen, it scrolls to the right. I thought it looked remarkably similar to @LivingEdge_Studios original list, it’s at least a useful subset, I think, to start from.
You’ve left out C7b9, C7#9, C7susb9b13, C7susb9#11b13, C7sus#9, C13sus#9, C7sus#9b13, C9sus#11, C13sus#9#11,Augmented 6th chords, Quartal chords, Quintal Chords, etc
Yes a lot of us can work these out on paper , but the reason we use apps like Scaler is to write faster and find sonorities and progressions we might not easily come up with…
I understand. Just thinking of ways how this can be accomplished as workaround until the full-fledged feature is there. I had the same interest, and I put it together by the various steps of picking scales, variations. To me, doing some of the work manually is part of my learning process. If I would be presented with a huge list of combinations, I would tune out.
But I hear you on the search feature. It would be cool to narrow down chord selections with various conditions/tags, such as show me all C chords that are augmented, but in a given scale outside of C, or something such. If the list of “all chords with the note C in it” is too long, having filter criteria becomes essential. Should be doable.
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I have a small program that does all this and more, called Chords ands Scales.
http://www.desktopmetronome.com/wpsite/products/chords-scales/
It tells me that C appears in the F# Symmetrical Diminished Minor scale, not that that is of interest. I can check on 82 other scales and all the modal variation thereof and will give me the degree of any note selected. (C is the fifth degree that scale.)
It’s useful for a guitarist.
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I don’t see enough interest in this topic. What interest there is, seems to me to be scattered with no one consensus of how to do things.
Personally, I thought that the OP’s request was rather straight forward. But even then came accusations of you forgot this, and you forgot that from the OP.
Sharkey 
waters! I’m pulling the plug on this…
I’m happily retired and don’t mind helping out, but I don’t work for you and am not a slave.
tl;dr The interest in this is too fragmented.
I still think it would be a good feature…