Consistency of the symmetric partition relation $\omega_2\to(\alpha)^2_2$ for all $\alpha<\omega_2$ (Erdős #1170)

For an ordinal $\kappa$ and a target order type $\alpha$, the partition arrow $\kappa\to(\alpha)^2_2$ asserts that whenever the $2$-element subsets of a set of order type $\kappa$ are coloured with $2$ colours, there exists a subset of order type $\alpha$ all of whose pairs receive a single colour (a monochromatic, or homogeneous, set). Here $\omega_2$ is the initial ordinal of the cardinal $\aleph_2$, and the subscript $2$ counts the colours. Is it consistent with ZFC that $$\omega_2\to(\alpha)^2_2$$ holds for every ordinal $\alpha<\omega_2$? Equivalently: is there a model of set theory in which every $2$-colouring of the pairs from an $\omega_2$-ordered set produces, for each prescribed $\alpha<\omega_2$, a monochromatic subset of order type $\alpha$?

Acceptance. FULLY RESOLVES: either (a) exhibit a model of ZFC — via a forcing construction, a clearly stated large-cardinal hypothesis, or an inner-model argument — in which $\omega_2\to(\alpha)^2_2$ holds simultaneously for every $\alpha<\omega_2$, with a complete proof (machine-checkable in Lean/Coq preferred, otherwise a full written proof); or (b) prove in ZFC that $\omega_2\not\to(\alpha)^2_2$ for some $\alpha<\omega_2$, refuting even consistency. ADVANCES (each with a complete proof): improve the best stated asymmetric consistency result by enlarging the fixed first coordinate beyond Foreman–Hajnal's $\omega_1^2+1$ while retaining $\omega_2\to(\cdot,\alpha)^2$ for all $\alpha<\omega_2$; or establish the symmetric relation $\omega_2\to(\alpha)^2_2$ consistently for all $\alpha$ in a specified unbounded subclass of $\omega_2$; or derive new ZFC-provable necessary conditions on any $\alpha$ for which the relation can hold. Deliver the forcing model / consistency proof or the ZFC (non-)implication with its full argument.