fix: harden and simplify Linux system install

Tighten shim detection, profile repair, and install ordering while
trimming over-specific doctor/info hints from the system-install path.

Co-authored-by: Cursor <cursoragent@cursor.com>

internal/shim/path_test.go

@@ -58,6 +58,11 @@ func TestFilterPMGFromPath(t *testing.T) {
 			shimEnv:  "/usr/local/lib/pmg/bin/npm",
 			expected: "/usr/local/bin:/usr/bin",
 		},
+		{
+			name:     "system shim dir is stripped without env var",
+			path:     "/usr/local/lib/pmg/bin:/usr/local/bin:/usr/bin",
+			expected: "/usr/local/bin:/usr/bin",
+		},
 		{
 			name:     "env var strips arbitrary shim dir",
 			path:     "/shims:/usr/local/bin:/usr/bin",