There are a few different definitions floating around the past few years. There are different concepts and components that can be qualified as atomic/immutable, sometimes joined together, sometimes not. It's a patchwork.

I'm not a fan for example of the universal package managers, but I do see the appeal for certain things. Yet, I do enjoy relying on docker/container to test software without having to taint my system.
Similarly, immutable sometimes rhyme with reproducible, and I've seen a lot of people enjoy NixOS and the Nix package manager. There's an appeal to having separate versions of the same software and swapping them whenever you feel like it. Personally, it was way too heavy and complex for me to run.
Furthermore, you need to add to these the idea of a system core that is the same for everyone, versioned (signed too), and having the user changes separate from it. The atomic updates. Things like homed, projects like os-tree, etc.. I like the concept, but personally I don't rely on these, I just manually keep track of my stuff.
With all that when things are containerized they often can't talk through the usual channels so you need a common communication which in this case is always dbus. This comes with standards like desktop-portals, polkit for security, pipewire for the media pipeline, etc.. I do think that's a good direction for the Linux desktop, building on the freedesktop standards.

With all this, there's also the secure distros that are somewhat immutable because they choose to run everything within VMs, like QubeOS. I've never tried it, but I'm wondering how fast of a machine you need to be able to do that. Maybe someone can enlighten us on this.