Hi,
It can be done by adding an event to the systray button.
For example, you can use the below code in .js

odoo.define('top_bar_button.systray_button', function (require) {
   "use strict";

   var core = require('web.core');
   var SystrayMenu = require('web.SystrayMenu');
   var Widget = require('web.Widget');
   var QWeb = core.qweb;
   var ajax = require('web.ajax');

var MySystrayWidget = Widget.extend({
   template: 'my_systray',
   events: {
       "click .systray_click": 'button_click'
   },

   button_click: function (e) {
       var self = this;
       e.preventDefault();
       self.do_action({
           name: 'The name of wizard',
           type: 'ir.actions.act_window',
           res_model: 'model of wizard',
           view_type: 'form',
           view_mode: 'tree,form',
           view_id: 'view id of wizard',
           views: [[false, 'list'], [false, 'form']],
           target: 'new'
       }, {
           on_reverse_breadcrumb: function () {
               self.update_control_panel({clear: true, hidden: true});
           }
       });
   }
});
SystrayMenu.Items.push(MySystrayWidget);
});