Build UK programme statistics from the model's own tax and benefit totals, not a fixed list #723

Problem

The UK program_statistics (the detailed_budget the apps chart as "Budgetary impact by programme") come from a fixed list of 14 programmes in src/policyengine/tax_benefit_models/uk/analysis.py. The headline budgetary_impact is the change in household_tax - household_benefits, and policyengine-uk builds those totals from HOUSEHOLD_TAX_VARIABLES (27 taxes) and HOUSEHOLD_BENEFIT_VARIABLES (about 50 benefits).

Any change in a programme outside the fixed list is in the headline but has no row, so the programme chart does not add up to the total and does not say why. The fixed list also has rows that are not in the total (ni_employer, vat, the overlapping tax_credits).

Example: the 2027 UC freeze (live report)

Report: https://app.policyengine.org/uk/report/49a9d5d0-85d7-4f95-b96e-eb26441e4191 (v1 report 4738). Reproduced locally on policyengine 6.10.0, policyengine-uk 2.132.6 and the certified microcosm_uk_2024_25.h5:

The £25.0m is Scottish Child Payment lost by Scottish families whose UC falls to zero (SCP is passported on UC).

On test households (84 families, Scotland and England, £0-£50k earnings), a 10% cut to the PIP standard daily living rate gives no rows at all with the fixed list (the whole impact is unexplained), and one pip row with rows from the totals.

Proposal

Build the UK rows from the variables the headline sums, not from a fixed list:

• Taxes: policyengine_uk.variables.gov.hmrc.household_tax.HOUSEHOLD_TAX_VARIABLES
• Benefits: policyengine_uk.variables.household.income.household_benefits.HOUSEHOLD_BENEFIT_VARIABLES

Return a row for each one that changes. The rows then add up to the headline by construction (apart from the gov.contrib.benefit_uprating contrib terms, which are zero by default), and a new benefit in policyengine-uk shows up with no change here. The model already computes these variables to get the totals, so the extra cost is small.

Points to settle:

1. Grouping. Programmes that move together can show as large bars that cancel out. With a £1,000 cut to the personal allowance, test households moved between extended_childcare_entitlement (+£10,234) and targeted_childcare_entitlement (-£10,234). A small grouping map (for example all childcare entitlements as one row) would avoid this.
2. Labels. Rows should carry the variable label so consumers do not hard-code names.
3. Compatibility. Keep the existing keys for the current programmes so saved outputs and the v2 chart still read.

The app will show any remaining gap as an "Other programmes" bar, so the chart always adds up even before this lands.