Add variable lookup tool after compiled variable metadata exists

[anth-volk]

Problem

UK Chat should eventually be able to answer questions such as:

• what does income_tax calculate?
• which entity does Universal Credit live on?
• what variables are available for a programme?
• what formula/source definition is associated with a variable?

However, the chat backend currently uses policyengine_uk_compiled as its calculation source of truth, and the compiled package does not yet expose a variable metadata/formula catalog. Pulling variable metadata and formulas from the separate policyengine_uk package would risk showing users metadata that diverges from the compiled engine actually used for calculations.

Dependency

Blocked on PolicyEngine/policyengine-uk-v2#106 exposing machine-readable variable metadata from policyengine_uk_compiled, especially:

• canonical variable name
• label/title
• entity
• description/definition
• input/output/intermediate status where available
• formula/source reference where feasible

Suggested scope after the dependency lands

• Add a lookup_variable model-facing tool backed by policyengine_uk_compiled metadata.
• Support exact variable names and deterministic natural-language matching.
• Return needs_confirmation with ranked options when the string match is ambiguous.
• Clearly label formula/source fields according to the compiled package contract.
• Add unit tests for exact, natural-language, ambiguous, and unknown variable queries.
• Add eval coverage across tool_contract, trajectory, and answer so model responses do not over-claim source/formula certainty.

Out of scope

Do not source variable formulas from policyengine_uk in UK Chat unless the product explicitly accepts that divergence risk.

[vahid-ahmadi]

Review: current main already exposes search_variables and get_variable backed by compiled model metadata, so the lookup portion of this issue has landed under different names. Before closing, compare the present get_variable response with the remaining formula/source-reference criterion; if authoritative source references are still unavailable upstream, narrow this issue to that single dependency rather than duplicating the shipped lookup feature.