[FEATURE] Support resuming previous chat sessions in Claude Code browser interface

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

Feature Request
When using Claude Code via the browser interface, there is currently no way to resume a previous conversation session. The CLI supports --resume and --continue flags for this, but the browser interface lacks equivalent functionality.

Current Workaround
Use the CLI with claude --resume or claude --continue instead of the browser interface.

Proposed Solution

Ability to list previous sessions from the claude code browser UI
Option to resume or continue a selected session, preserving full conversation context
Ideally parity with the CLI's --resume and --continue functionality

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

CLI commands and flags

Use Case Example

Long-running tasks or multi-step workflows where remote sessions may be closed or refreshed
Returning to a session after stepping away
Maintaining context continuity without re-explaining prior work

Additional Context

_No response_