fix(examples-py): validate OpenLIT, OpenRouter, and PGVector OTel 2.x spans

[Nightingalelyy]

Summary

• Add complete OpenLIT and PGVector example suites and expand OpenRouter to deterministic sync, async, stream, tool, error, and explicit real-provider coverage.
• Preserve exact run markers, local editable-package verification, bounded semantic roots, portable requirements, timeout aggregation, and explicit teardown.
• Keep OpenRouter scenarios 01–07 deterministic even when a credential exists; scenario 08 alone validates the live provider.

Validation

• Example contract tests: OpenLIT 10/10, OpenRouter 15/15, PGVector 10/10.
• Root-scoped Ruff check and format check pass for all three example directories.
• All 17 scripts completed under otel2-fix-py-group-21-20260817T214109Z; the PGVector live-database script reported its intended missing-DSN skip.
• Respan MCP returned 16 trace trees and 48 full details with exact marker propagation, one root per trace, valid parentage, unique IDs, bounded content, correct streams, tools, errors, and no credential leakage.
• Live OpenRouter scenario returned live OpenRouter verified with exact non-estimated 15/4/19 usage.

External follow-ups

• Real PostgreSQL/pgvector execution remains gated by PGVECTOR_DSN.
• Upstream OpenAI/httpx2/httpcore2 [DONE] async teardown behavior is covered separately; deterministic stream fixtures drain through EOF.

Companion examples

• Source instrumentation PR: fix(instrumentation-py): repair OpenLIT, OpenRouter, and PGVector OTel 2.x spans respan#387