How to append a specific string to a URL that matches, constantly with Tampermonkey? Or another method?

Question

I want to append this string:

&sp=CAASAhAB

Every time a YouTube search query is performed to remove that stupid "People also watched" section.

I've created a Tampermonkey script that works pretty well but does not work when the search is performed by the website's own search box.

Could anyone help? Solving this would be great for posterity's sake.

Here's the TamperMonkey script:

// ==UserScript==
// @name         Youtube - Remove "People Also Watched" section from search results.
// @namespace    http://tampermonkey.net/
// @version      1.1
// @description  Add "&sp=CAASAhAB" to YouTube search results URL if not already present. Recommended to also use https://github.com/Vulpelo/hide-youtube-shorts
// @author       MattFor | @mattfor | https://github.com/MattFor
// @match        www.youtube.com/results?search_query=*
// @grant        none
// ==/UserScript==

(function () {
    "use strict";

    function containsString(mainString, subString) {
        return mainString.indexOf(subString) !== -1;
    }

    function updateURL() {
        var currentURL = window.location.href;
        var queryString = "&sp=CAASAhAB";

        if (!containsString(currentURL, queryString)) {
            window.location.href += queryString;
        }
    }

    updateURL();

    window.addEventListener("beforeunload", updateURL);
    window.addEventListener("DOMContentLoaded", updateURL);
})();

---

Edit #1: Updated my code based on comments to the question yet there are no significant upgrades, looks like the YouTube POST request is only sent once judging by the network tab.

// ==UserScript==
// @name         Youtube - Modify search request
// @namespace    http://tampermonkey.net/
// @version      1.1
// @description  Add "&sp=CAASAhAB" to YouTube search results URL if not already present.
// @author       MattFor | @mattfor | https://github.com/MattFor
// @match        www.youtube.com/results?search_query=*
// @grant        none
// ==/UserScript==

(function () {
    "use strict";

    function containsString(mainString, subString) {
        return mainString.indexOf(subString) !== -1;
    }

    function updateURL() {
        var currentURL = window.location.href;
        var queryString = "&sp=CAASAhAB";

        if (!containsString(currentURL, queryString)) {
            window.location.href += queryString;
        }
    }

    function modifySearchForm() {
        var searchForm = document.getElementById("search-form");

        if (searchForm) {
            searchForm.addEventListener("submit", function (event) {
                event.preventDefault();
                var formAction = searchForm.action;
                var modifiedAction = formAction + "&sp=CAASAhAB";
                searchForm.action = modifiedAction;
                searchForm.submit();
            });
        }
    }

    updateURL();
    modifySearchForm();

    window.addEventListener("beforeunload", updateURL);
    window.addEventListener("DOMContentLoaded", function () {
        updateURL();
        modifySearchForm();
    });
})();