It's available as a technical preview in Safari, and Mozilla in nightly builds only, according to what I could find. Support in Chrome/-ium was removed December 2022 with no news of any change as far as I could see, so Chromium-based browsers won't have support, from what I understand. You could use an extension for Chrome to add support, but, as a content provider/site owner, you can't rely on users and visitors installing that to view your site properly, of course.
I'm not telling you to lose hope. I still have hope too. But don't invest time and effort into JXL if you want to serve images online. Not until promises of widespread support from all major parties. At least not on the web. If you plan on sending files to people, then sure.
All the best to you!