Flatpak permissions are very broad by default in most applications. Even if you manually override them by using Flatseal, some permissions like X.org or PulseAudio sockets are very problematic because these legacy protocols are not designed to be secure. Even if you manage to lock down permissions and only use modern apps that support Wayland and Pipewire, the Flatpak sandbox still exposes a lot of kernel attack surface because it blocks very few syscalls. I think they should add something similar to Win32k lockdown (ProcessSystemCallDisablePolicy) on Windows and disable insecure components like io_uring.

As for immutable distros, AFAIK Silverblue and others are immutable in the sense of package management, but there is actually no process to ensure the integrity of the full boot chain because initrd can be trivially modified by the host and is unsigned. There is a UKI (Unified Kernel Image) proposal that will likely be the path going forward (at least on the Red Hat world), but I think it's still years away.

In my opinion, if you want to use Linux desktop securely, just use Qubes.