refactor(OperatorAlgebra): Implement states in more Mathlib-aligned style (RFC)

[goliath-klein]

This is an RFC. The intention is to suggest a way for implementing basic notions of QM in a way that minimizes diverges from Mathlib definitions and style.

More here.

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[morrison-daniel]

Is this ready for review, or just shared for discussion? If we are waiting to review then could we mark this as a draft for now?

[goliath-klein]

Converted to draft pending Zulip discussion.