Seeming as I'm getting downvoted, let me explain my point better -- and please hear me through because I'm genuinely making some balanced arguments here rather than just viewing things as "black and white":
If you care about security enough to be concerned about memory-safety bugs in tmux, then tmux is already a fail, regardless of whether it's written in Rust. I detailed some features in another comment about some of tmux's features that basically make it spyware for untrusted code. And that's got nothing to do with the language it is written in.
But assuming you only care about terminal output and trust the software you execute, then you still have a hundred other libraries written in C between and tmux and the internet: openssh, libcurl, openssl, glibc, and so on and so forth. I'd actually welcome seeing many other those rewritten in Rust (or another memory safe language). So rewriting tmux before them is a lot like closing the barn door after the horse has already bolted.
Thus if you're genuinely concerned about memory safety security vulnerabilities then the only safe way to work with untrusted output is in a VM.
As it happens, this is exactly how highly secure systems operate. Their developers work on VMs which are tightly locked down by the vendor and easy to destroy if they become compromised.
Literally the only way to solve the problem you describe is to assume the entire stack is already compromised and thus run it in a sandbox.
So does rewriting tmux in Rust improve security? Yes, technically you're right. But it makes almost zero practical benefit compared to everything else. Memory-safety in tmux is not your weak link here. Not even remotely.
Disclaimer: I've developed terminal emulators, shells and terminal multiplexers in memory safe languages. My latest project makes heavy use of tmux integrations (again, in a memory safe language) so I'm very familiar with tmux's quirks. I also have a background in DevSecOps. You could almost say this topic is my specialist subject ;) The Rust hype is a generally good thing but misplaced in this very specific discussion.