feat: POST /log from the page + load state.json on page open

- Browser can record entries (e.g. meter readings) into session.md/jsonl;
  broadcast to other open clients. Log feed renders as text, not HTML.
- Page loads state.json on open instead of only localStorage, so a new
  device (or one that missed the WS push) shows current content.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

tests/test_server.py

@@ -124,3 +124,19 @@ async def test_static_blocks_path_traversal(server, tmp_workbench):
         async with session.get(base + "/") as r:
             assert r.status == 200
     await server.workbench_stop("p")
+
+
+@pytest.mark.asyncio
+async def test_browser_post_log_persists_and_broadcasts(server, tmp_workbench):
+    from workbench.project import read_log
+    session, base = await _live(server)
+    async with session:
+        ws = await session.ws_connect(base + "/ws")
+        async with session.post(base + "/log", json={"entry": "R303 3.31M", "data": {"part": "R303"}}) as r:
+            assert r.status == 200
+        msg = await asyncio.wait_for(ws.receive_json(), 3)
+        assert msg == {"type": "log", "entry": "R303 3.31M"}
+        await ws.close()
+    entries = read_log("p", workbench_dir=tmp_workbench)
+    assert entries[-1]["entry"] == "R303 3.31M" and entries[-1]["part"] == "R303"
+    await server.workbench_stop("p")