Excluding individual page components from caching

I can't seem to find a straight answer online about whether it is possible to exclude just one component of a page from being cached.

My component appears on all pages of the site and comes from a custom theme function rendered in page.html.twig from the following in mytheme_preprocess_page:

$alerts_renderable = [
'#theme' => 'my_alerts',
];
$variables['alerts'] = $alerts_renderable;

I've tried adding #cache => ['max-age' => 0] in that render array to no effect. I read elsewhere that changing max-age has no effect on anonymous visitors. Has anyone had success in ever doing this?

The component is an alert bar that site admins can enter text via a settings page on the backend. That message appears in the alert bar on every page of the site. Currently, when admins change the message, it requires a cache clear for the new message to be publicly visible

The current limitations on the max-age implementation are documented, as are the workarounds.

Until these (and perhaps other) issues are resolved, beware that setting max-age on a render array included in a page is insufficient to ensure that anonymous users will see a new version after the max-age as elapsed. In the meanwhile, the Cache Control Override contributed module tries to mitigate the problems. You might also have more luck setting a custom cache tag on pages with time-dependent content and invalidating those cache tags manually via hook_cron(). Good luck!

The paragraph above contains hyperlinks to the referenced resources when viewed on the documentation page.