[FEATURE] Apply user-level CLAUDE.md and rules to cloud sessions (web / mobile)

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When Claude Code runs on Anthropic-managed cloud infrastructure — via claude.ai/code,
the iOS app, or claude --remote — the session sandbox has no access to the user's
~/.claude/ directory. Only the repository-level CLAUDE.md is loaded (cloned from
GitHub). As a result, personal coding standards, style preferences, and behavioral rules
defined globally by the user are silently absent from every cloud session.

This is distinct from cross-machine sync requests (see #22648, #19634, #6037): those
address replicating local config between machines. This request addresses cloud sessions
where there is no local machine in the picture at all — the sandbox is ephemeral and
user-owned files never exist on it. Even if account-level sync (#6037) were implemented,
it would not cover this case: there is no local Claude Code process in the sandbox to
perform a sync operation.

Proposed Solution

When a cloud session starts, Claude Code could inject the authenticated user's
account-level instruction files into the session context. The user's Anthropic account
already authenticates the session; this data could be fetched from account storage at
session init.

Proposed scope

In scope — secret-free markdown instruction files:

| File | Notes |
|------|-------|
| ~/.claude/CLAUDE.md | Plain instructions, no secrets |
| ~/.claude/rules/*.md | Same nature as CLAUDE.md, modular |
| ~/.claude/skills/*/SKILL.md | Instruction layer only (see open question below) |

Explicitly out of scope:

| File | Reason |
|------|--------|
| ~/.claude/settings.json | May contain secrets via the env block |
| ~/.claude.json | OAuth tokens, MCP credentials |
| ~/.claude/skills/*/ supporting files | See open question below |

Open question: skill supporting files

Skills can include non-markdown supporting files (scripts, binaries, data). Three options:

1. Markdown-only: upload SKILL.md instructions but skip supporting files — skills

that depend on them degrade gracefully

1. Upload everything: let supporting files be present in the sandbox, fail at runtime

if dependencies are missing

1. User-declared: let users mark skills as "cloud-compatible" in frontmatter

Option 2 raises a legitimate concern: running arbitrary user-uploaded scripts on
Anthropic infrastructure may be outside the intended security model of the sandbox.
Leaving this open for Anthropic to weigh in on.

Alternative Solutions

Commit a CLAUDE.md to every repository. This is per-project, not per-user. It pollutes repos with personal preferences that don't belong in shared version control, and doesn't cover rules and skills.

Priority

High - Significant impact on productivity

Feature Category

Configuration and settings

Use Case Example

A developer maintains a global ~/.claude/CLAUDE.md enforcing personal coding
standards (commit style, language preferences, review checklist). When working locally,
every session respects these rules automatically. When delegating a task to a cloud
session from their phone — a bug fix on a repository that has no project-level CLAUDE.md
— the rules are silently absent. The cloud agent produces output inconsistent with the
developer's established standards, requiring manual correction after the fact.

Additional Context

Related issues

• #22648 — Account-level settings sync across machines (broader, local-to-local)
• #19634 — Account-level CLAUDE.md (duplicate of above, auto-closed)
• #6037 — Add account settings config layer