fix(cursor): remove stale ~/.cursor/bin references missed in #3058 migration

Clean up three remaining stale references to ~/.cursor/bin that were
not caught in the #3058 path migration:

- manifest.json: update notes field to reflect ~/.local/bin/agent
- sh/e2e/lib/provision.sh: remove ~/.cursor/bin from path_prefix
- sh/e2e/lib/verify.sh: remove ~/.cursor/bin from binary check PATH

Fixes #3065

Agent: issue-fixer
Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

Author: louisgv

manifest.json

@@ -332,7 +332,7 @@
           }
         }
       },
-      "notes": "Works with OpenRouter via --endpoint flag pointing to openrouter.ai/api/v1 and CURSOR_API_KEY set to OpenRouter key. Binary installs to ~/.cursor/bin/agent.",
+      "notes": "Works with OpenRouter via --endpoint flag pointing to openrouter.ai/api/v1 and CURSOR_API_KEY set to OpenRouter key. Binary installs to ~/.local/bin/agent.",
       "icon": "https://raw.githubusercontent.com/OpenRouterTeam/spawn/main/assets/agents/cursor.png",
       "featured_cloud": [
         "digitalocean",

sh/e2e/lib/provision.sh

@@ -378,7 +378,7 @@ _ensure_agent_binary() {
   # PATH includes all common binary locations for detection.
   local bin_name=""
   local install_cmd=""
-  local path_prefix='export PATH="$HOME/.npm-global/bin:$HOME/.bun/bin:$HOME/.local/bin:$HOME/.cargo/bin:$HOME/.claude/local/bin:$HOME/.cursor/bin:/usr/local/bin:$PATH"'
+  local path_prefix='export PATH="$HOME/.npm-global/bin:$HOME/.bun/bin:$HOME/.local/bin:$HOME/.cargo/bin:$HOME/.claude/local/bin:/usr/local/bin:$PATH"'
 
   case "${agent}" in
     claude)

sh/e2e/lib/verify.sh

@@ -755,7 +755,7 @@ verify_cursor() {
 
   # Binary check — cursor installs to ~/.local/bin/agent (since 2026-03-25)
   log_step "Checking cursor binary..."
-  if cloud_exec "${app}" "PATH=\$HOME/.local/bin:\$HOME/.cursor/bin:\$HOME/.bun/bin:\$PATH command -v agent" >/dev/null 2>&1; then
+  if cloud_exec "${app}" "PATH=\$HOME/.local/bin:\$HOME/.bun/bin:\$PATH command -v agent" >/dev/null 2>&1; then
     log_ok "cursor (agent) binary found"
   else
     log_err "cursor (agent) binary not found"