This is the beginnings of Google Meets integration with Jabra headsets.

jabra.googlemeets.user.js

// ==UserScript==
// @name        Jabra - Google Meets
// @namespace   Violentmonkey Scripts
// @match       https://meet.google.com/*
// @grant       none
// @version     1.0
// @author      -
// @description 19/09/2021, 11:53:37
// @requireingore https://cdnjs.cloudflare.com/ajax/libs/jquery/3.2.1/jquery.min.js
// @requireignore https://cdnjs.cloudflare.com/ajax/libs/toastr.js/latest/js/toastr.min.js
// @require https://cdn.jsdelivr.net/npm/@violentmonkey/dom@1
// @require https://raw.githubusercontent.com/gnaudio/jabra-browser-integration/master/src/JavaScriptLibrary/jabra.browser.integration-3.0.js
// @require https://raw.githubusercontent.com/f3oall/awesome-notifications/master/dist/index.var.js
// @run-at document-end
// ==/UserScript==

/**
* Requirements:
* You must install the following Jabra things first:
* * Jabra ChromeHost - https://developer.jabra.com/site/global/software/integration-components/browser/index.gsp
* * Jabra Browser Integration Extension - https://chrome.google.com/webstore/detail/jabra-browser-integration/okpeabepajdgiepelmhkfhkjlhhmofma
*
* Jabra have some documentation about the browser extension here: https://developer.jabra.com/site/global/software/integration-components/browser/documentation.gsp
* and they have a sample Javascript page you can use to test out that the extension is working correctly: https://gnaudio.github.io/jabra-browser-integration/release/development/
*/

// var newCSS = GM_getResourceText ("awesomeCss");
// GM_addStyle (newCSS);
// debugger;
function addCss(cssUrl) {
  let link = document.createElement("link")
  link.rel  = 'stylesheet';
  link.type = 'text/css';
  link.href = cssUrl;
  link.media = 'all';
  document.head.appendChild(link);
}
addCss('https://f3oall.github.io/awesome-notifications/assets/css/style.css?v=8a1d3104c509964ebd7ff91202b41c936df37f48')

var toastr = {
    info: (msg) => {
        // Awesome notifications isn't working anymore due to some TrustedHtml error, I guess google meets changed.
        // new AWN().info(msg, {icons: {enabled: false}})
        console.log(msg);
    }
}

// console.log("Jabra should be here now");

function showError(err) {
    let msg;
    if (err.name === "CommandError" && err.errmessage === "Unknown cmd" && err.command === "getinstallinfo") {
        msg = "Could not lookup installation info - Your installation is incomplete, out of date or corrupted.";
    } else if (err instanceof Error) {
        msg = err.toString();
    } else if ((typeof err === 'string') || (err instanceof String)) {
        msg = err;
    } else {
        msg = JSON.stringify(err);
    }

    // Add nodes to show the error message
    // var div = document.createElement("div");
    // var att = document.createAttribute("class");
    // att.value = "wrapper";
    // div.setAttributeNode(att);
    // div.innerHTML = msg;
    // var br = document.createElement("br");
    // var list = document.getElementById("section");
    // list.insertBefore(br, list.childNodes[0]);
    // list.insertBefore(div, list.childNodes[0]);

    toastr.info(msg);
}

function setupDevices() {
    jabra.getDevices().then((devices) => {
        console.log(devices);
    });
}

// Refresh device list automatically when devices are inserted/removed:
jabra.addEventListener(["device attached", "device detached"], (event) => {
    setupDevices();
});

var micNode = undefined;

window.addEventListener('beforeunload', () => {
    jabra.onHook();
})

jabra.addEventListener("mute", (event) => {
    console.log("mute button clicked")
    if (micNode) {
        let isMicMuted = micNode.getAttribute('data-is-muted').toLowerCase().indexOf('true') !== -1
        if (!isMicMuted) {
            micNode.click();
        }
    }
});

jabra.addEventListener("unmute", (event) => {
    console.log("unmute button clicked")
    if (micNode) {
        let isMicMuted = micNode.getAttribute('data-is-muted').toLowerCase().indexOf('true') !== -1
        if (isMicMuted) {
            micNode.click();
        }
    }
});

// Use the Jabra library - to be sure of the installation we also check it and report errors
// This installation check is optional but is there to reduce support issues.
jabra.init().then(() => jabra.getInstallInfo()).then((installInfo) => {
    if (installInfo.installationOk) {
        toastr.info("Jabra library initialized successfully");

        setupDevices();

        VM.observe(document.body, () => {
            // Find the target node
            const node = document.querySelector('[data-is-muted][role=button]')

            if (node) {
                micNode = node;
                jabra.offHook();
                VM.observe(node, () => {
                    console.log("Mic button changed")
                    let isMicMuted = node.getAttribute('data-is-muted').toLowerCase().indexOf('true') !== -1
                    if (isMicMuted) {
                        jabra.mute();
                    } else {
                        jabra.unmute();
                    }
                }, {
                    childList: false,
                    subTree: false,
                    attributes: true,
                    attributeFilter: ['data-is-muted']
                })
                // disconnect observer
                return true;
            }
        });

    } else { // Installation not ok:
        showError("Installation not ok - Your installation is incomplete, out of date or corrupted.");
    }
}).catch((err) => {
    showError(err);
});