feat(web): continue branches across environments

[jln13x]

Problem

A thread and its work can live on a remote environment even when the user wants to continue the pushed branch on another connected machine. Moving the full conversation is covered by the broader direction in pingdotgg#2829, but branch-only handoff can be useful independently.

Solution

• add a Continue branch on… submenu for matching repository projects on connected environments
• open a fresh destination draft without copying conversation history
• fetch origin on first send and check out the same branch name in a destination worktree
• reuse an existing destination checkout, while treating the primary checkout as local so it cannot be mistaken for a removable worktree
• expose the action in the chat header and both web/desktop sidebar implementations

Testing

• 92 focused web tests passed
• 44 contract tests passed
• contracts, server, and web typechecks passed
• targeted lint and formatting passed
• added a focused server integration test; its local execution was blocked before assertions by an environment-level EDQUOT error while the test secret store was being created

Screenshots

Omitted at maintainer request.

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