Userscript for current site search with selection search chrome extension. Tested with Violenmonkey.

search-current-site.js

// ==UserScript==
// @name         Search with the first input found on current site
// @namespace    https://github.com/Pitmairen/selection-search
// @version      0.1
// @description  Use search url: #_selectionsearch_=%s With icon url: CURRENT_DOMAIN 
// @author       Pitmairen
// @license      GPL-3.0
// @match        *://*/*
// @homepageURL  https://chrome.google.com/webstore/detail/selection-search/gipnlpdeieaidmmeaichnddnmjmcakoe
// @supportURL   https://github.com/Pitmairen/selection-search/issues
// @run-at       document-idle
// @grant none
// ==/UserScript==
(function() {
    'use strict';

    var selectors = [
        'input[id*="search"]',
        'input[class*="search"]',
        'input[type="search"]',
        'form[class*="search"] input[type="text"]',
        'form[id*="search"] input[type="text"]',
        'form[action*="search"] input[type="text"]',
        'input[name="q"]',
    ];

    var overrides = {
        'forum.vivaldi.net': (input) => {
            input.form.action = '/search';
            input.name = 'term';
        },
    };

    var separator = '_selectionsearch_=';

    var doSearch = () => {
        if(location.hash.indexOf(separator) !== -1){

            var input = document.querySelector(selectors.join(','));

            if(input != null){

                var query = decodeURIComponent(location.hash.split(separator)[1]);

                input.value=query;

                if(location.host in overrides){
                    overrides[location.host](input);
                }

                input.form.submit();
            }
        }
    }
  
    window.addEventListener('hashchange', doSearch);
  
    doSearch();
})();