The way you present "immutable distros" make them look like state-of-the-art stateless systems (a la NixOS with the impermanence module).
As much as I'd wish (so-called) immutable distros were like that, almost none of them actually are^[It's basically the aforementioned NixOS. And, even then, only if you've set it up like that. Guix System might offer it as well, but I couldn't verify it the last time I looked into it.].
Fedora Atomic, which may or may not have surpassed NixOS in popularity by now, practically just locks down /usr. That's cute, but it means that the immutability doesn't prevent persistence of hardware in most of the filesystem.
Similarly, I could go over the other popular immutables to point out how their immutability doesn't do much to combat persistence. But I digress...
OP, I'll keep it short as you might have already moved on. Security on desktop Linux isn't great. The lack of widespread sandboxing is one of the main culprits. Good 'hygiene' should keep you safe. But, if you're (rightfully) more concerned, then I'd suggest looking into secureblue^[Note: this distro might be hard to get into if it's your first distro. Consider joining community channels for assistance.].