[FEATURE] Add ability to delete individual sessions from claude.ai/code web UI

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

Currently, there is no way to delete individual Claude Code sessions from
the web UI at claude.ai/code. When I use /clear or delete local session
history through Claude Code CLI, those sessions remain visible and
accessible on the web at claude.ai/code. This is a privacy and
organization concern — I cannot manage or clean up my cloud-stored
session history without contacting Anthropic support directly.

<img width="926" height="797" alt="Image" src="https://github.com/user-attachments/assets/c7bfd02b-bd82-48d7-aa11-9161b5b2cd1d" />

Proposed Solution

Add a delete button (or trash icon) next to each session listed on the
claude.ai/code sessions page. Ideally:

1. A per-session delete option visible on hover or via a "..." menu
2. A confirmation prompt before deletion to prevent accidental removal
3. Optionally, a "Delete all sessions" bulk action

The experience should mirror how other tools (e.g., ChatGPT, Gemini)
allow users to delete individual conversation history entries.

Alternative Solutions

• Contacting Anthropic support to request manual deletion — not scalable

or user-friendly for routine session management

• Using account-level data deletion — too broad, removes everything

rather than specific sessions

• Local /clear command — only removes local history, does not affect

cloud-stored sessions at claude.ai/code

Priority

High - Significant impact on productivity

Feature Category

CLI commands and flags

Use Case Example

1. I finish working on a client project and want to remove that session

from my cloud history for privacy

1. I go to claude.ai/code and find the session
2. Currently there is no delete button — I am stuck with it permanently

in my session list

1. With this feature, I could click delete on that specific session and

confirm removal

1. This would give users control over their own data without needing

to contact support

Additional Context

The local CLI command /clear does not sync with the web — this creates
a confusing disconnect where users believe they've deleted their history
but it remains visible on the web. A delete option on claude.ai/code
would close this gap.