Rust is pretty clear about “safe” meaning no memory unsafety in unsafe-free code. It certainly doesn't market that code without unsafe will be bug free (this would force the safe subset to no longer be Turing complete).
It can still be surprising because in other languages it may be the case that a stack overflow can lead to memory unsafety. However, in Rust, a stack overflow leads to a guaranteed abort on major platforms, and a best-effort abort on niche platforms (the reason being that LLVM only provides stack probes for major platforms, so niche platforms have to make do with only guard pages).
I'm unclear how that would lead to undefined behavior on stack overflow. Stack overflow on Rust is specified to immediately abort the entire process (with some aforementioned wrinkles as to how achievable that is on certain targets), which necessarily nukes all TLS.
The fact that the linked issue isn't tagged with "I-unsound" suggests that nobody has ever indicated that that might somehow be a soundness issue. If you think otherwise, I encourage you to bring it up so that any soundness issue can be properly tracked.
To push this point a little further: in Rust when there's not a clean way to prevent memory unsafety (or when you haven't requested to), it aborts the process. Out of array indexing, stack overflows, etc.
Minor clarification: there's a difference between a "panic" (which may either unwind or abort, based on compilation flags) and a "guaranteed abort" (which is not negotiable). Array-index-out-of-bounds is merely a panic, as are almost all "unrecoverable errors" in Rust. Things that are guaranteed to abort are rare in Rust; I can only think of stack overflows, and OOM for certain stdlib types.
I think we're lucky the usual "aha rust isn't so safe after all, checkmate rustaceans!" crowd hasn't run into these aborts yet, because they won't have any kind of debugging spew so are not very friendly. You have to intentionally leak refcounts to hit these aborts or else you first run out of memory just storing the pointers; but then again, intentionally leaking things is just the sort of thing the anti-rust crowd is likely to try.
As far as I know, in the case of stack overflow, the code that aborts the process should literally just be a single line of assembly that contains an invalid opcode, resulting in a (safe) segfault. What has given you the impression that there is potential for UB in these code paths?
Stack overflow in Rust does abort the process, but not immediately: the signal handler first distinguishes stack overflow from other sources of SIGSEGV/SIGBUS, and then prints a message containing the name of the current thread. Both of these require accessing TLS, which in turn may panic, or invoke other non-async-signal safe functions. That is UB.
I don't know what the definition of a "soundness issue" is, but I think there are some nasal demons to be found here; it will be fun to try at least.
edit the linked issue missed a case! Rust aborts by using libc::abort(), which is not async signal-safe in glibc prior to 2.26.
My point is more that debugging a core dump (and similar activities) would be all the more foreign. The engineer might even be shocked that the need to do that sort of thing even exists for a piece of Rust code.