[FEATURE] Rename claude code for web to "Cloude".

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

There is no consistent branding around what to call the cloud environment of Claude Code.

Proposed Solution

Claude is running in the cloud. It is short. It is quippy. It is difficult to typo ("a" is far from "o"). And, it allows clear distinction of which environment the agent is in without relying on a bunch of qualifiers that clog up context.

Alternative Solutions

Claude in the Cloud.
Cloud Claude.

Priority

Low - Nice to have

Feature Category

Other

Use Case Example

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Additional Context

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