For servers there's Docker/Kubernetes/Podman, which is well-established and serves a similar purpose as Flatpak on the desktop. Servers were actually first with the increase in popularity of containers.
90 % or more of my desktop (Fedora Kinoite and Silverblue) apps are Flatpaks already. I only have four rpm-ostree overlays (native packages) left: android-tools, brasero/k3b, syncthing (I could switch to SyncThingy for a Flatpak) and virt-manager/virtualbox
With Flatpak there is "flatpak override" which gives you the ability to grant additional permissions or restrict them even further. E. g. I use it to connect KeePassXC with Firefox or to disallow access to the X server to force almost all apps to use Wayland instead of X. It also allows me to prevent apps from creating and writing into arbitrary directories in my home.
Once I reinstall my home server, all its server software will be containerised as well (five years ago I didn't see the necessity yet). I am tired of having to manage dependencies with every (Nextcloud) upgrade. I want something that can auto update itself completely with minimal or no breakage, just like my desktops.
Have you considered a fixed release in combination with rolling applications (i. e. Flatpak, Snap)?
If you choose Fedora (preferably one of the atomic variants, like Silverblue), you would also get a rolling kernel and rolling KDE Plasma desktop, so overall the experience can be quite close to a rolling release distribution if you install the desktop applications via Flatpak.
Ubuntu "interim" (non-LTS) releases are usually also fairly current and could be a good choice if you don't mind Snap. There's also the option of following the Ubuntu "devel" branch, which always refers to the current pre-release version of Ubuntu (e. g. 24.04 at the moment) and is rolling.
Just wanted to give you a different direction to think about. ;)