Fixes#1913. The sign-in hint named the bare command (`cursor-agent login`), but the IDE launches agents through its own resolution (registry installs under the config dir, the login shell's PATH, PATHEXT shims), so the named command could be missing from the terminal's PATH. The agent spec is now resolved once before connecting, and when that executable isn't what a PATH lookup of the bare name finds, every built-in hint names the resolved path, quoted for PowerShell or POSIX shells. Hints for separate login tools (claude-acp, codex-acp, vibe) and custom agents are unchanged; the hint is translated through templates.