ViolentMonkey script for focussing search bars when you press tab.

focus-search.js

// ==UserScript==
// @name         Focus Search on Tab
// @namespace    http://tampermonkey.net/
// @version      1.0
// @description  Focus the main search input when Tab is pressed
// @match        *://*/*
// @grant        none
// ==/UserScript==

(function() {
    'use strict';

    document.addEventListener('keydown', (e) => {
        // Only trigger on Tab, and only if we're not already in an input/textarea
        if (e.key !== 'Tab') return;

        // Find search input with a simple heuristic
        const selectors = [
            'input[type="search"]',
            'input[name*="search" i]',
            'input[name*="query" i]',
            'input[id*="search" i]',
            'input[placeholder*="search" i]',
            'input[aria-label*="search" i]',
            'input[type="text"]',
            'div#prompt-textarea',
            'textarea',
            '*[contenteditable="true"]',
        ];

        const inputs = document.querySelectorAll(selectors.join(','));

        // Find first visible input
        for (let input of inputs) {
            if (input.offsetParent !== null && !input.disabled) {
                e.preventDefault();
                input.focus();
                return;
            }
        }
    });
})();