Since youtube sometimes changes the players’s behaviour, I’ll try to keep the code up to date and as robust as possible.
var settings_button = document.querySelector(".ytp-settings-button");
settings_button.click(); settings_button.click(); // open and close settings, so annotations label is created
var all_labels = document.getElementsByClassName("ytp-menuitem-label");
for (var i = 0; i < all_labels.length; i++) {
if ((all_labels[i].innerHTML == "Annotations") && (all_labels[i].parentNode.getAttribute("aria-checked") == "true")) { // find the correct label and see if it is active
all_labels[i].click(); // and in that case, click it
}
}