You can use js and buses like this:
1. Send a message from Python when something changes

self.env['bus.bus'].sudo()._sendone(
    'broadcast',
    'crm_stage_changed',
    {}
)

2. Subscribe to the bus event in JavaScript and reload the page when the message arrives:

/** @odoo-module **/

import { registry } from "@web/core/registry";

export const crmStageRefreshService = {
    dependencies: ["bus_service"],

    start(env, { bus_service }) {
        bus_service.subscribe("crm_stage_changed", () => {
            window.location.reload();
        });
    },
};

registry.category("services").add("crmStageRefresh", crmStageRefreshService);