fix(index): bound LLM concurrency at the leaf, not per gather call

The previous approach (bounded_gather building a fresh semaphore per call)
did NOT compose: the indexing call graph nests gathers
(tree_parser -> process_large_node_recursively -> recurse, plus each node's
check_title gather), and each level got its own independent cap. Peak
in-flight LLM calls grew ~N^depth, so a deep/wide document still exhausted
file descriptors (Errno 24) — the exact failure the cap was meant to
prevent — while the flat summary phase was over-serialized. Naively sharing
one semaphore across gather levels would instead deadlock (a parent holds a
slot while awaiting children that need slots).

Move the throttle to the single chokepoint every LLM call funnels through,
llm_acompletion: one shared semaphore per event loop, acquired only around
the litellm.acompletion network call. This gives a true global cap that
composes across any nesting and can't deadlock (a parent awaiting children
holds no slot). bounded_gather is gone; the call sites revert to plain
asyncio.gather.

Also:
- Reject bool in max_concurrency validation (bool is an int subclass, so
  set_max_concurrency(True) / IndexConfig(max_concurrency=True) previously
  became Semaphore(1) and silently serialized). Shared _validate_max_concurrency
  + a pydantic field_validator.
- Guard check_title_appearance_in_start_concurrent against an out-of-range
  or 0 physical_index (LLM can emit one): it was dereferenced during task
  construction, outside the gather's return_exceptions protection, aborting
  the whole build; 0 silently wrapped to the last page. Now marked 'no'.
- Propagate contextvars into agent.py's worker-thread run (mirrors
  pipeline._run_async) so ContextVar settings stay consistent.
- Tests rewritten to cover the nested case the old flat tests missed, the
  leaf-level throttle in llm_acompletion, bool rejection, and the
  out-of-range physical_index guard.

Claude-Session: https://claude.ai/code/session_01Kx5DgKbhK1N8autqXH8SmS

tests/test_pipeline.py

@@ -93,3 +93,22 @@ def test_null_logger_methods():
     logger.error("test error")
     logger.debug("test debug")
     logger.info({"key": "value"})
+
+
+def test_check_title_appearance_tolerates_out_of_range_physical_index():
+    """An LLM-emitted physical_index outside page_list must be marked 'no', not
+    raise IndexError (which happens during task construction, outside the
+    gather's return_exceptions protection, and would abort the whole build)."""
+    from pageindex.index.page_index import check_title_appearance_in_start_concurrent
+
+    page_list = [("only page text", 3)]  # length 1
+    structure = [
+        {"title": "A", "physical_index": 5},     # out of range -> would IndexError
+        {"title": "B", "physical_index": 0},     # 0 -> would wrap to page_list[-1]
+        {"title": "C", "physical_index": None},  # missing
+        {"title": "D"},                          # no physical_index key at all
+    ]
+    result = asyncio.run(
+        check_title_appearance_in_start_concurrent(structure, page_list)
+    )
+    assert all(item["appear_start"] == "no" for item in result)