[Feature Request] Add session deletion UI to VS Code extension and CLI

Bug Description
Title: Feature Request: Easy session deletion in VS Code extension

Body:

Currently there is NO way to delete sessions in Claude Code (VS Code extension or CLI).
Users have to manually edit JSON files in ~/.claude/ and ~/.claude.json, which is:

• Error-prone (can break JSON syntax)
• Tedious (need to find correct file, reload VS Code)
• Not discoverable (users don't know where files are stored)

VS Code Copilot handles this much better - users can easily delete conversations from the UI.

Requested features:

1. Right-click "Delete" option in session picker dropdown
2. /delete command to remove current or specific session
3. Bulk delete option for old sessions
4. "Clear all sessions" option in settings

This is basic session management that users expect from a chat-based tool.

Environment Info

• Platform: win32
• Terminal: null
• Version: 2.1.20
• Feedback ID: 297931b2-8cdb-4d27-a499-f4874deaa812

Errors

[{"error":"Error: ENOENT: no such file or directory, scandir 'C:\\ProgramData\\ClaudeCode\\.claude\\skills'\n    at readdirSync (unknown)\n    at <anonymous> (B:/~BUN/root/claude.exe:12:2063)\n    at tX (B:/~BUN/root/claude.exe:11:35584)\n    at readdirSync (B:/~BUN/root/claude.exe:12:2024)\n    at x3$ (B:/~BUN/root/claude.exe:1756:380)\n    at x3$ (B:/~BUN/root/claude.exe:1756:1350)\n    at <anonymous> (B:/~BUN/root/claude.exe:1756:4670)\n    at <anonymous> (B:/~BUN/root/claude.exe:1756:5401)\n    at A (B:/~BUN/root/claude.exe:11:7259)\n    at qOE (B:/~BUN/root/claude.exe:4824:4342)","timestamp":"2026-01-29T16:48:32.598Z"},{"error":"Error: ENOENT: no such file or directory, scandir 'C:\\Users\\fitra\\.claude\\skills'\n    at readdirSync (unknown)\n    at <anonymous> (B:/~BUN/root/claude.exe:12:2063)\n    at tX (B:/~BUN/root/claude.exe:11:35584)\n    at readdirSync (B:/~BUN/root/claude.exe:12:2024)\n    at x3$ (B:/~BUN/root/claude.exe:1756:380)\n    at x3$ (B:/~BUN/root/claude.exe:1756:1350)\n    at <anonymous> (B:/~BUN/root/claude.exe:1756:4713)\n    at <anonymous> (B:/~BUN/root/claude.exe:1756:5401)\n    at A (B:/~BUN/root/claude.exe:11:7259)\n    at qOE (B:/~BUN/root/claude.exe:4824:4342)","timestamp":"2026-01-29T16:48:32.598Z"},{"error":"AbortError: The operation was aborted.\n    at unknown\n    at abortChildProcess (node:child_process:947:42)\n    at onAbortListener2 (node:child_process:35:24)\n    at abort (unknown)\n    at <anonymous> (B:/~BUN/root/claude.exe:3025:209)","timestamp":"2026-01-29T16:48:34.148Z"}]