[FEATURE] Show Local / SSH hostname label next to project group name in sessions panel

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

In the Claude Code sessions panel, project groups are only labeled by their local folder name (e.g. my-local-folder). When working across multiple machines via SSH, there is no way to tell at a glance whether a project group belongs to the local machine or a remote SSH host — you have to click into each session to find out.

This is especially painful when the same folder name exists on both local and remote hosts.

Proposed Solution

Display a small Local or SSH hostname badge next to (or below) the project group name in the sessions panel. For example:

my-local-folder    [Local]
my-dev-server-folder    [dev-server]
my-project    [build-machine]

The label would use:

• Local for sessions running on the local machine
• The SSH hostname (from sshConfigs[].name or the host address) for remote sessions

Related Issues

• #52690 — Show git branch in remote SSH workspace chip row (similar "more context in UI" direction)
• #51028 — SSH sessions feature parity with local sessions

Use Cases

• Quickly distinguish local vs remote project sessions at a glance
• Users managing the same codebase across multiple machines (e.g. local laptop + remote dev server)
• Prevent accidentally sending prompts to the wrong environment