Run desktop app sessions inside the repo's dev container

Feature request. The redesigned Claude Code desktop app orchestrates parallel sessions, but every session runs on the host. I'd like the option to run each session inside the repo's dev container instead, for isolation and reproducibility.

Proposed behavior:

• On opening a repo, detect a .devcontainer/devcontainer.json.
• Offer, opt-in, to build and run that dev container as the session's execution environment.
• Run Claude Code inside the container — just as VS Code's "Reopen in Container" does locally — so the agent only touches mounted project files.
• Support this per-session, so parallel sessions can each run in their own container.

Why: the ghcr.io/anthropics/devcontainer-features/claude-code feature already means Claude Code is designed to run inside a dev container. The missing piece is letting the desktop app use that container as its session environment. This would give desktop sessions parity with the local VS Code dev container workflow, and let users safely run bypass-permissions mode without the agent reaching the host.

Note: issue #47856 requests this for Claude Code on the web. This request is specifically for the desktop app