It's more about parallelism than asynchronousness. (They're certainly related, but the CDN argument related to limits on multiple downloads from the same origin is about parallelism.)
How can I make the page download the scripts asynchronously, but execute them synchronously?
Any decent browser, when given the three script tags you've shown, will download them in parallel (up to its parallel-from-the-same-site limit) and then execute them in order. You don't have to do anything to make that happen. Browsers read ahead in the HTML to find resources to fetch.
Adding fallback scripts with document.write
might complicate the browser's ability to do that, or even prevent it, but you can ensure it declaratively using <link rel="preload" as="script" href="...">
(more on MDN). Combining that with fallback scripts for failed CDN resources, it might look something like this:
<head>
<!-- ... -->
<link rel="preload" as="script" href="//ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js">
<link rel="preload" as="script" href="//cdnjs.cloudflare.com/ajax/libs/popper.js/1.16.0/umd/popper.min.js">
<link rel="preload" as="script" href="//maxcdn.bootstrapcdn.com/bootstrap/4.5.2/js/bootstrap.min.js">
</head>
<body>
<!-- ... -->
<script src="//ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<script>if (!/*loaded condition*/) document.write(/*fallback*/);</script>
<script src="//cdnjs.cloudflare.com/ajax/libs/popper.js/1.16.0/umd/popper.min.js"></script>
<script>if (!/*loaded condition*/) document.write(/*fallback*/);</script>
<script src="//maxcdn.bootstrapcdn.com/bootstrap/4.5.2/js/bootstrap.min.js"></script>
<script>if (!/*loaded condition*/) document.write(/*fallback*/);</script>
</body>
</html>
Note that that doesn't preload the fallbacks. You could, but then you'd be loading them even when the CDN was working, which wastes the end user's bandwidth. The fallbacks would be for the presumably-temporary degraded situation where the CDN was unavailable, where a degraded user experience is probably okay. (You could even show the user an indicator of a problem when scheduling the fallback, like Gmail's "something is taking longer than usual" indicator.)
If you're bothered by repeating the URLs and you're okay with document.write
in small doses (as you seem to be), you can avoid duplicating the URLs by doing something along these lines:
<head>
<!-- ... -->
<script>
var scripts = [
{
url: "//ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js",
okay: function() { return /*check it loaded*/; }
},
{
url: "//cdnjs.cloudflare.com/ajax/libs/popper.js/1.16.0/umd/popper.min.js",
okay: function() { return /*check it loaded*/; }
},
{
url: "//maxcdn.bootstrapcdn.com/bootstrap/4.5.2/js/bootstrap.min.js",
okay: function() { return /*check it loaded*/; }
},
];
scripts.forEach(function(script) {
document.write('<link rel="preload" as="script" href="' + script.url + '">');
});
</script>
</head>
<body>
<!-- ... -->
<script>
scripts.forEach(function(script, index) {
var fallback = script.url.substring(script.url.lastIndexOf('/') + 1);
document.write('<script src="' + script.url + '"><\/script>');
document.write('<script>if (!scripts[' + index + '].okay()) document.write(\'<script src="' + fallback + '"><\\/script>\');<\/script>');
});
</script>
</body>
</html>
(Since that's all inline script you're unlikely to transpile, I've kept the syntax to ES5 level in case you have to support obsolete environments.)