Fix pointer navigation in Quattro launcher menus (#6343)

Accumulate sub-threshold movement so slow motion with a flat acceleration profile updates selection. Sample pointer state on row entry and carry pointer intent through subordinate menus while preserving predictable keyboard selection.

test/shell.d/pointer-move-gate-test.sh

@@ -25,12 +25,51 @@ assert(
   /function reset\(\)[\s\S]*root\.primed = false/.test(gateQml),
   'pointer movement gate can be disarmed after keyboard or list changes'
 )
+assert(
+  /function reset\(\)[\s\S]*root\.initialSampleAllowed = false/.test(gateQml),
+  'reset keeps the initial pointer sample ignored by default'
+)
+assert(
+  /function allowInitialSample\(\)[\s\S]*root\.reset\(\)[\s\S]*root\.initialSampleAllowed = true/.test(gateQml),
+  'pointer-initiated transitions can opt in to the initial pointer sample'
+)
 assert(
   /item\.mapToItem\(target, mouse\.x, mouse\.y\)/.test(gateQml),
   'pointer movement gate compares movement in stable target coordinates'
 )
 assert(
-  /var didMove = root\.primed[\s\S]*Math\.abs\(point\.x - root\.lastX\) > root\.threshold[\s\S]*Math\.abs\(point\.y - root\.lastY\) > root\.threshold/.test(gateQml),
-  'pointer movement gate only reports real movement after an initial sample'
+  /var didMove = !firstSample[\s\S]*Math\.abs\(point\.x - root\.lastX\) > root\.threshold[\s\S]*Math\.abs\(point\.y - root\.lastY\) > root\.threshold[\s\S]*root\.initialSampleAllowed/.test(gateQml),
+  'pointer movement gate reports real movement or an explicitly allowed initial sample'
+)
+assert(
+  /if \(firstSample \|\| didMove\) \{\s*root\.lastX = point\.x\s*root\.lastY = point\.y\s*\}/.test(gateQml),
+  'sub-threshold pointer movement accumulates from the last accepted sample'
+)
+assert(
+  /root\.primed = true\s*root\.initialSampleAllowed = false/.test(gateQml),
+  'the initial pointer sample exception is consumed once'
 )
 JS
+
+if ! command -v quickshell >/dev/null 2>&1; then
+  pass "quickshell not installed; skipping pointer movement gate runtime test"
+  exit 0
+fi
+
+test_tmp=$(mktemp -d)
+trap 'rm -rf "$test_tmp"' EXIT
+
+cp "$SHELL_TEST_DIR/fixtures/pointer-move-gate/shell.qml" "$test_tmp/shell.qml"
+ln -s "$ROOT/shell/Ui" "$test_tmp/Ui"
+
+output=$(timeout 15 quickshell -p "$test_tmp" --no-color 2>&1) || {
+  printf '%s\n' "$output" >&2
+  fail "pointer movement gate runtime fixture exits cleanly"
+}
+
+if ! grep -q "RESULT pass" <<<"$output"; then
+  printf '%s\n' "$output" >&2
+  fail "pointer movement gate runtime behavior is correct"
+fi
+
+pass "pointer movement gate runtime behavior is correct"