fix(frontend): deep-linked switches frozen — commit selection via History API

[bvdmitri]

Problem

Opening a shared link that already carries query params (e.g.
https://benchmarks.rxinfer.com/?b=basic%2Fcoin_toss&hw=rpi5-8gb) left every
selector dead — the hardware/Julia/scenario/metric switchers and the left sidebar
examples. Selecting anything did nothing. Starting fresh from the bare
benchmarks.rxinfer.com (no params) worked. First reported in Safari, but reproduces
in Chrome too.

Root cause

All dashboard state lives in query params via useSelection(), and every selector
funnels through its single select() function, which committed each change with
router.replace(...). That runs the App Router's navigation/transition machinery. On
this static export (output: "export"), a query-only router.replace on a
deep-linked load silently no-ops — no exception, it just doesn't navigate, so
useSearchParams() never updates and the controlled <Select>s/buttons stay frozen.
One broken commit function = every selector frozen at once.

Fix

Commit selections with window.history.replaceState instead of router.replace.
Next.js syncs useSearchParams/usePathname with pushState/replaceState and skips
the route transition — the documented idiom for query-param-only state updates. URL
building is unchanged; replaceState (no new history entry) preserves the prior
router.replace behavior.

Verification

• Unit: useSelection + DashboardPage tests updated to assert on history.replaceState; full suite 161 passing, tsc + eslint clean.
• End-to-end in real headless Chromium against a production static build (data from raw.githubusercontent.com), opening the exact deep link above:

	Hardware switch	Sidebar example
Old router.replace	URL unchanged ❌	URL unchanged ❌
Fixed history.replaceState	hw=rpi5-8gb → hw=github-actions-ubuntu ✅	b=coin_toss → b=iid_normal ✅

No console/page errors in either build.

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