[FEATURE] Register as VS Code inline chat edit tool provider

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

VS Code's inline chat panel ("Modify selected code", triggered by selecting code) supports pluggable providers. Claude Code does not register as one, so the panel shows "MISSING inline chat edit tools" and Claude Code is unavailable there.

The key value of that panel is contextual hand-off — VS Code can automatically inject why an edit is needed (lint diagnostics, PR review comments, diff context) without the user having to re-explain it. The current workaround of Alt+K to reference a selection in the Claude Code panel loses that automatic context.

Proposed Solution

Implement the VS Code InlineEditProvider (or equivalent chat participant with @workspace /fix style edit capability) so Claude Code appears as an option in the inline chat tool picker and receives the editor-provided context automatically.

Alternative Solutions

Currently using Alt+K to reference the selection in the Claude Code panel, then manually describing why the edit is needed. This works but requires re-stating context that VS Code already has (e.g. the failing diagnostic, the PR comment that prompted the change). GitHub Copilot solves this by registering as an inline chat provider and receiving that context automatically.

Priority

Medium - Would be very helpful

Feature Category

Developer tools/SDK

Use Case Example

1. I'm reviewing a PHP file and the linter flags a type error on a selected line
2. I press Ctrl+. or the inline chat shortcut — VS Code opens the "Modify selected code" panel with the diagnostic pre-loaded as context
3. With Copilot this auto-populates the prompt with the error; with Claude Code the panel shows "MISSING inline chat edit tools" and I have to switch to the Claude Code sidebar, re-type the error manually, and reference the selection via Alt+K
4. The desired flow: Claude Code appears in the provider list, receives the diagnostic context automatically, and I just hit enter

Additional Context

The VS Code API for this is vscode.InlineEditProvider, introduced in VS Code 1.93. A provider registered via vscode.languages.registerInlineEditProvider receives a InlineEditContext containing the triggering diagnostic or selected range, which is exactly the contextual hand-off that's missing today.

GitHub Copilot implements this — it appears in the same "Modify selected code" dropdown as a reference implementation.