The amount of untrusted code running in browser is only increasing over time, and the CPU vendors have absolutely noticed this. That's why ARMv8.3A added an instruction that literally has JavaScript in it's name (FJCVTZS) for instance.
Once you have mitigations for colocating trusted and untrusted code in ring 3, doing the same in ring 0 almost certainly isn't a big deal.
In-process sandboxing by all appearances is simply dead.
As for "doing the same in ring 0 almost certainly isn't a big deal" no, very extremely no. If you let code run in ring 0 it has everything ring 0 can do, period. You cannot put restrictions on it, that's what spectre proved. Give code access to a process and it has entire access to that process. Similarly give something ring 0, and it has the entirety of ring 0.
Untrusted code goes in ring 3 in an isolated process. That's the security model of x86, and it's the only model that CPU vendors have any pressure to fix.
Chip vendors have & will fix process boundaries. But nobody is talking about any sort of protection of any kind that would let in-process sandboxing work again. It's just not even on the table at this point.
I do not think there is the degree of distinction between "processes" and "threads" that you think there is. If tools exist to isolate speculation state between processes, those tools can probably also isolate threads in a process.
There's no particular reason to believe this. Neither Intel nor AMD have committed to any form of side-effect-free speculative execution or similar. That'd required a rather large chunk of transistors and die space, and if nobody is footing the bill for it it's not going to happen.
Preventing side-effects from leaking between processes (and ring levels) entirely at the hardware level is definitely going to happen. Within a process, though? That's not going to happen without multiple major players demanding it. Since nearly all the major CPU consumers are currently happy with process boundaries being the security enforcement zones, there's no particular reason to believe that in-process sandboxing will ever have hardware fixes to prevent spectre attacks.