Not just Chromium-based browsers, Firefox as well. Might not make much of a difference for user counts but it does mean that so far it's available on the web is limited to a single vendor.
It's worth noting that it is "supported" in Firefox however it's not enabled at compile time for release builds (but is enabled for nightly and testing/validation builds).
Full release/production support will come when the (more or less drop in replacement) rust rewrite of libjxl is production ready.
Firefox has it implemented (behind a preference on nightly). They just don't want to ship it if Chromium isn't going to because it would cause fragmentation in the web and something they have to maintain forever for a minority of sites (as most won't bother if Chromium based browsers don't support it).
Tbh it's less about having to maintain it forever and more about not wanting to deal with maintaining a C++ library codebase that would widen the potential attack surface of the browser (due to memory bugs, etc). They are fine adopting it as long as it's in rust (which is being worked on, see sibling comments)
The Mozilla "organizations" are a two-headed grift piggy-backed on a non-profit shell so the IRS keeps smiling.
Firefox hasn't made a technical decision without first forwarding the minutes to Mountain View and Redmond since roughly 2017.
Every nine-figure Google wire lands promptly converts into $450 k-per-head salary vapor and off-site "all-hands," while the same week another 250 actual engineers get an email that begins: "You're talented and valued BUT-."
Servo? Jettisoned.
MDN? Gutted.
Security teams? Re-org'd into a Slack channel no one reads.
And the Foundation helpfully reminds donors:
"Your gifts don't pay for Firefox engineering."
No kidding. They pay for glossy pamphlets proclaiming the open-web gospel, first-class flights to "advocacy summits," and Mitchell Baker's $2.5 million thank-you note. Firefox isn't a browser; it's a loss-leader Google keeps in the closet for the next antitrust subpoena.
So does Chrome if you check out the right commits and enable it.
But if you go getfirefox.com, click "Download Firefox" then there will be no JXL support not even behind any configuration flags. So no, it doesn't support it. There are also no plans to enable support with the current implementation.