I would appreciate someone else who knows more than me about the current state of these attacks and more than me about Linux security in general answering this question. Take what I'm about to say with a grain of salt.

My understanding is that Firefox still reduces timer accuracy, Chrome did, but increased timer accuracy again after adding other protections. I'm not sure if Chrome's protections rely on Meltdown vulnerabilities being patched on the OS level or not. It's been a while since I checked back on what the status was there, so I might be wrong.

There are also some concerns about shared memory buffers, which is why I think some of the features around them haven't been enabled in WASM yet. I haven't checked the status on that stuff in a while either.

In any case, for a vulnerability of this scale I bias towards saying people should practice defense in depth. Sometimes browsers have bugs in them, and this would be a particularly bad one. And again, there are userland native apps and systems and package managers that people need to worry about that go beyond browsers.