capital_income leaves out other_investment_income, and no test checks household net income for it #2745

#2736 counts other_investment_income in market_income, household_market_income and HBAI income. Two pieces are still missing.

capital_income leaves it out.

• capital_income is "Income from savings or dividends". It adds savings_interest_income, tax_free_savings_income, dividend_income and individual_savings_account_dividend_income.
• Other investment income is interest on National Savings products, gilts and other securities, and from trusts. Income tax charges it as savings income (taxable_savings_interest_income).
• So £2,000 of bank interest gives £2,000 of capital income, but £2,000 of gilt interest gives nil.
• No formula reads capital_income, so only that output is wrong. Tax, benefits and the other income measures don't move.

No test checks household net income.

• The bug in household_market_income leaves out other_investment_income, which income tax charges #2733 showed up in household_net_income. Take an employee on £40,000 of pay with £2,000 of other investment income in 2026-27. Before Count other investment income in market and HBAI income #2736 their household net income was £31,939.60, less than the £32,139.60 they had with no interest.
• Count other investment income in market and HBAI income #2736's YAML checks market income, HBAI income and tax, but not household_net_income or household_gross_income.
• No test checks that the two kinds of interest move every income measure alike.

Proposal.

• Add other_investment_income to capital_income, next to savings_interest_income.
• Check capital_income, household_gross_income and household_net_income in other_investment_income_in_household_income.yaml.
• Add a property test, at several pay levels in England and Scotland. The same interest, as bank interest or as other investment income, should give the same income tax and the same market, capital, gross, net and HBAI income. Market and capital income should rise by the interest. Net and HBAI income should rise by the interest less its tax.