feat: URL state persistence for all filters and tabs

CLAUDE.md

@@ -643,6 +643,42 @@ Local `.md` sidecars can annotate remote activities.
 - The `site/.env` file is gitignored — document the setup for new users
 - Add `--workers` benchmark: on 8 cores, ~7 min for 3,200 activities first run
 
+## URL state — design pattern
+
+All pages with filter or tab state persist it in the URL query string so the browser
+back button restores the exact view. The pattern used in every component:
+
+```ts
+let mounted = false;
+
+$: if (mounted) {
+  const params = new URLSearchParams(window.location.search);
+  if (value === DEFAULT) params.delete('key'); else params.set('key', value);
+  const qs = params.toString();
+  history.replaceState(null, '', qs ? `?${qs}` : window.location.pathname);
+}
+
+onMount(() => {
+  value = new URLSearchParams(window.location.search).get('key') ?? DEFAULT;
+  mounted = true;
+});
+```
+
+Key decisions:
+- `replaceState` not `pushState` — clicking filters doesn't create history entries; back always goes to the previous *page*, not previous filter state
+- `mounted` flag — prevents the reactive block from firing before `onMount` reads the URL (which would overwrite the URL with the default before reading it)
+- Default values omitted — `?sport=all` and `?tab=power` are never written; clean URLs
+
+Current URL params:
+| Page | Param | Values |
+|------|-------|--------|
+| `/` (feed) | `sport` | `cycling`, `running`, etc. |
+| `/stats/` | `sport` | same |
+| `/athlete/` | `tab` | `records`, `profile` (power is default) |
+| `/athlete/?tab=records` | `sport` | `cycling`, `swimming`, etc. (running is default) |
+
+If you add a new filter to any page, follow this pattern. Never use `pushState` for filter changes.
+
 ## What "good" looks like (not yet done)
 
 - [ ] `bincio render` Python CLI wraps `astro build` properly