fix: review round 2 — per-browser UA cache, leak fixes, docs

[desperatee]

Summary

• CRITICAL fix: UA cache moved from global package variable to per-browser sync.Once — fixes incorrect cache sharing across browsers with different versions/channels, eliminates global mutex contention at scale
• HIGH fix: Context leak in NewStealthPage when NewPage() fails
• HIGH fix: Panic-safe type assertion in getPatchedUA
• HIGH fix: routeInjecting flag reset on Route() failure so retries work
• Docs: README updated with stealth API section, CLAUDE.md updated with new files, LLM guide and example updated

Review findings addressed

#	Severity	Issue	Fix
1	CRITICAL	Global patchedUACache wrong for multi-browser fleets	Per-browser sync.Once on browserImpl
3	HIGH	NewStealthPage leaks context on NewPage failure	context.Close() on error path
4	HIGH	Unchecked type assertion can panic in getPatchedUA	Comma-ok form + error return
4b	HIGH	ctx.Close() errors silently discarded	Logged via package logger
5	HIGH	routeInjecting stuck on Route() failure	Reset to false on error

Test plan

• All unit tests pass
• Integration test passes
• E2E: Walmart homepage returns 200 with stealth page
• go build ./... and go vet ./... clean