Add three EntitledTo-style integration tests (#778) (#1713)

#778 asks for ~20 worked benefit scenarios checked against EntitledTo.
This is a first batch of three covering the most common household
shapes the calculator handles:

1. single 30-year-old working part-time on low pay, private renter in
   London (UC + child benefit zero, no income tax/NI),
2. couple with two children, one earner at £22k, social housing in
   North West (UC + child benefit, partial NI/income tax),
3. pensioner couple with low state pension, sits below Pension Credit
   guarantee level (PC payout + winter fuel allowance).

Values are pinned to the current PolicyEngine output and the file is
labelled as a regression-grade baseline rather than an authoritative
EntitledTo cross-validation — future work is to manually re-run the
matching cases through EntitledTo and tighten any rows where the two
disagree, ratcheting up to the ~20-scenario coverage in the issue.

Person-level variables (income_tax, national_insurance) can't be
asserted with a single scalar when multiple people are in the benunit,
so scenario 2 uses household_tax instead.

Author: vahid-ahmadi

changelog.d/778.md

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+- Add three worked benefit scenarios at `policyengine_uk/tests/policy/integration/entitledto_scenarios.yaml` as a first batch of EntitledTo-style regression tests (single low-earner private renter, couple with two children in social housing, pensioner couple on the Pension Credit guarantee), seeding the ~20-scenario coverage suggested in #778.

policyengine_uk/tests/policy/integration/entitledto_scenarios.yaml

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+# Worked benefit scenarios for cross-checking against EntitledTo
+# (https://www.entitledto.co.uk/), tracked in issue #778.
+#
+# These are pinned to PolicyEngine's current outputs and serve as
+# regression tests rather than authoritative EntitledTo matches: the
+# numbers were generated by running each scenario through PolicyEngine
+# at the time the file was added. Future work is to manually run the
+# matching cases through EntitledTo and tighten any rows where the two
+# disagree, ratcheting up to the ~20-scenario coverage suggested in #778.
+
+- name: "EntitledTo #1 - single 30yo working part-time at low pay, private renter in London"
+  period: 2025
+  absolute_error_margin: 1
+  input:
+    people:
+      adult:
+        age: 30
+        employment_income: 12_000
+    benunits:
+      benunit:
+        members: [adult]
+    households:
+      household:
+        members: [adult]
+        rent: 8_000
+        council_tax: 1_200
+        region: LONDON
+        country: ENGLAND
+        tenure_type: RENT_PRIVATELY
+  output:
+    income_tax: 0
+    national_insurance: 0
+    universal_credit: 3_662.72
+    housing_benefit: 0
+    child_benefit: 0
+    household_net_income: 14_303.68
+
+- name: "EntitledTo #2 - couple with 2 children, one earner at £22k, social housing in North West"
+  period: 2025
+  absolute_error_margin: 1
+  input:
+    people:
+      adult_1:
+        age: 35
+        employment_income: 22_000
+      adult_2:
+        age: 35
+      child_1:
+        age: 5
+      child_2:
+        age: 3
+    benunits:
+      benunit:
+        members: [adult_1, adult_2, child_1, child_2]
+    households:
+      household:
+        members: [adult_1, adult_2, child_1, child_2]
+        rent: 6_000
+        council_tax: 1_500
+        region: NORTH_WEST
+        country: ENGLAND
+        tenure_type: RENT_FROM_COUNCIL
+  output:
+    # Household-level aggregates only — per-person income_tax / NI can't be
+    # asserted with a single scalar when multiple people are in the benunit.
+    household_tax: 4_047.45
+    universal_credit: 12_490.86
+    housing_benefit: 0
+    child_benefit: 2_251.60
+    household_net_income: 36_130.40
+
+- name: "EntitledTo #3 - pensioner couple, low state pension, qualifies for Pension Credit"
+  period: 2025
+  absolute_error_margin: 1
+  input:
+    people:
+      pensioner_1:
+        age: 70
+        state_pension: 8_000
+      pensioner_2:
+        age: 68
+        state_pension: 6_000
+    benunits:
+      benunit:
+        members: [pensioner_1, pensioner_2]
+    households:
+      household:
+        members: [pensioner_1, pensioner_2]
+        region: WEST_MIDLANDS
+        country: ENGLAND
+        council_tax: 1_800
+  output:
+    universal_credit: 0
+    housing_benefit: 0
+    pension_credit: 3_607.72
+    winter_fuel_allowance: 200
+    income_tax: 0
+    national_insurance: 0
+    household_net_income: 15_848.68