Support nested CLAUDE.local.md discovery in subdirectories

Feature Request

Support discovering CLAUDE.local.md files in nested subdirectories, similar to how CLAUDE.md files are discovered.

Current Behavior

Per the Memory documentation:

"Claude will also discover CLAUDE.md nested in subtrees under your current working directory. Instead of loading them at launch, they are only included when Claude reads files in those subtrees."

This nested subtree discovery is documented for CLAUDE.md but not for CLAUDE.local.md. Testing confirms CLAUDE.local.md files are only loaded at the project root level.

Proposed Behavior

CLAUDE.local.md files should also be discovered in nested subdirectories, loaded on-demand when Claude reads files in those subtrees (matching the behavior of nested CLAUDE.md discovery).

Use Case

In monorepos or projects with distinct subsystems, users may want personal/private instructions for specific parts of the codebase without:

• Polluting shared CLAUDE.md files with personal preferences
• Committing personal workflow notes to version control

Examples:

• client/CLAUDE.local.md - personal frontend testing preferences or debugging notes
• server/CLAUDE.local.md - personal backend development context
• packages/auth/CLAUDE.local.md - personal notes about a complex subsystem

Why This Makes Sense

The rationale for nested CLAUDE.md discovery applies equally to CLAUDE.local.md:

"Different parts of a monorepo might have different conventions"

If hierarchical team instructions are valuable, hierarchical personal instructions are too. The only difference is whether they're shared (tracked in git) or personal (gitignored).

Current Workarounds

None are ideal:

• Using nested CLAUDE.md with personal content and adding to .gitignore is awkward (CLAUDE.md is conventionally tracked)
• Putting everything in root CLAUDE.local.md doesn't scale for large projects
• Path-specific rules in .claude/rules/ don't support user-level configs