fix(ui): reconcile partial-month cost maths + add period navigation

[albinati]

Why

A review of the home dashboard surfaced wrong financial maths: for the current (in-progress) month the standing charge was billed for the full calendar month (monthrange() days) while energy/import/export covered only elapsed days. Effects:

• Hero "net bill so far" inflated by (remaining_days × standing) (~£11.50 on the 2nd of a month).
• "Saved vs Fixed" understated / flipped (counterfactual used elapsed-day standing, realised used full-month).
• CostBreakdown standing bar ~15× too tall early in the month (full-month standing ÷ elapsed days).
• Same bug inflated the tariff-comparison table standing + the "last Nd of usage" label.

Two secondary axis inconsistencies were folded in per the agreed scope: realised export billed at a flat rate (should be per-slot Outgoing Agile), and the savings calc mixing Fox-metered vs Octopus-metered kWh.

Separately, the user asked for day/week/month/year navigation across the dashboard.

Backend — cost-axis reconciliation (src/energy/)

• Standing proration: new n_days arg on _compute_cost / _compute_cost_octopus / _best_cost (defaults to full month → completed past months byte-for-byte unchanged). Month/year/day/week branches + get_monthly_insights pass the elapsed-day count, clamped to today.day (robust to Fox zero-padding).
• Realised export now billed at per-slot Outgoing Agile rates (reuses the pnl.py:_realised_export_pence pattern via db.get_agile_export_rates_in_range), not a flat manual rate.
• Fixed-tariff shadow (fixed_shadow_*, delta_vs_fixed_*) computed on the same metered kWh + day-window as realised cost — kills the Fox-vs-Octopus mix. day/week now route realised cost through the Octopus per-slot engine too (manual fallback preserved for un-backfilled days).
• tariff_engine._get_usage_data prorates total_days for the current month.
• New fields exposed on the cost response (src/api/models.py, src/api/main.py).

Frontend — shared period navigator (ui/)

• New lib/period.ts signal + PeriodNavigator (‹ label › + day/week/month/year toggle) drives the whole page; "next" disabled at the current period.
• Hero re-scopes to the selected period and uses the backend delta_vs_fixed_pounds (drops the client-side Fox-kWh savings recompute); adds a "live now" strip that ignores the selector.
• CostBreakdownChart renders the selected period (removes the month-avg-rate trailing-7d approximation).
• TariffComparisonWidget uses the backend fixed shadow for the fixed row (consistent with the realised current-tariff row).
• EnergyChartWidget reads the shared signal; navigating to a past day shows daily totals (per-slot history is still UI energy chart: capture per-30min solar / grid import / export for day-view breakdown #424).

Tests

• New tests/test_monthly_cost_proration.py: proration, past-month regression guard, per-slot export billing, fixed-shadow correctness, tariff-engine day count.
• Backend: all monthly/period/pnl/tariff/insights tests pass. UI: tsc --noEmit + npm run build clean.
• Pre-existing unrelated date-flakes (test_dhw_policy, test_pv_calibration_3d, test_tariff_aware_load_profile) fail on the base branch too.

Verification

• ✅ Backend unit tests (proration + regression guard) green.
• ✅ UI type-check + build green; API server boots, routes register.
• ⏳ Full end-to-end (real Fox/Octopus data) verifies on prod after deploy: current-month standing_charge_pence / chart_data.length ≈ standing/day, past month bills full month unchanged, navigator steps across all granularities, standing bar no longer towers early in the month.

No pre-existing tracking issue; touches the #424 per-slot-history area (navigator now allows past-day selection, flagged accordingly).

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