[BUG] No visual indicator for local vs cloud (web) session — beginners assume it works locally, wasting turns/tokens

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

When opening a Claude Code session, there is no visible indicator of whether it
runs locally (on my machine) or in a cloud / web environment.

This matters because the two have different filesystem access: a cloud session
cannot reach local files (e.g. ~/.claude/scheduled-tasks), so a request that
assumes local access silently fails and needs several back-and-forth turns to
diagnose.

What actually happened to me:
I opened a NEW Claude Code session from my iPhone, so it was a cloud session.
Later I sat down at my Mac and asked it to edit a local-only scheduled task — but
the session is still cloud and replied that it cannot access my Mac. The session
type is fixed at creation, so to work locally I had to open a brand-new session.
This back-and-forth (and the restart) wasted tokens.

Additional point (beginner perspective):
Because "Claude Code" is offered as a choice on iPhone / mobile, a new user
naturally assumes it will "just work" on their own machine. There is no cue that
this is a cloud session with no access to local files, so the user confidently
makes local-only requests that cannot succeed — and only finds out after wasting
several turns and tokens.

For beginners especially, the UI should make this self-evident WITHOUT needing an
explanation — e.g. a persistent badge like "Cloud — cannot access files on your
Mac" at session start, or a different name / icon for cloud vs local sessions.

Request:

• A clear, persistent badge on each session ("Local" vs "Cloud / Web").
• Ideally show the working directory / host at a glance.
• Make it obvious that session type is fixed at creation (and/or offer a way to

move a cloud session to local without starting over).

• Make the distinction understandable to a first-time user without reading docs.

Related: #57379, #22723

【要望】特にiPhoneからClaude Codeの新規セッションを開くとクラウドになり、途中で
Macの前に戻っても「自分のPCでは動かせない」と言われる。セッション種別が最初に
固定されるため、ローカルで作業するには新規セッションを開き直す必要があり、
トークンを無駄に消費する。セッションがローカルかクラウドか一目で分かるUI
（バッジ・名前/アイコンの区別・作業ディレクトリ表示）と、初心者でも説明なしで
分かる表示が欲しい。

What Should Happen?

When opening a Claude Code session, the UI should make it immediately obvious
whether the session runs locally (on my machine) or in the cloud / web — without
needing to ask or read docs.

Specifically:

• A clear, persistent badge on each session: "Local" vs "Cloud / Web".
• Show the working directory / host at a glance.
• Make it obvious that the session type is fixed at creation, and ideally offer

a way to move a cloud session to local without starting over.

• A first-time user (e.g. opening Claude Code from an iPhone) should understand,

before sending any request, that a cloud session cannot access their local
files — so they don't waste turns/tokens on requests that can't succeed.

セッションを開いた時点で、ローカルかクラウドか一目で分かるべき。バッジ表示・
作業ディレクトリ表示・種別が固定であることの明示・（できれば）クラウド→ローカル
への移行手段。初心者がトークンを無駄にする前に「クラウドはローカルファイルに
触れない」と分かる状態が理想。

Error Messages/Logs

Steps to Reproduce

This is a UX/design issue rather than a code bug, so specific reproduction
steps don't apply. The issue occurs whenever you open Claude Code from an
iPhone or web browser — the session is cloud, but there's no indication of
that fact.

Claude Model

None

Is this a regression?

No, this never worked

Last Working Version

_No response_

Claude Code Version

2.1.167 (Claude Code)

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

Terminal.app (macOS)

Additional Information

_No response_