Linux is a kernel, not an app platform. While you can use some apps across several different Linux-based OSes, many apps are only designed to integrate with a specific platform like GNOME, KDE, elementary OS, etc.
Ubuntu, one of the most popular Linux desktop distributions, uses their own Snap packaging technology and app store which is not included in any other Linux-based OS.
Some platforms like elementary OS AppCenter require apps to use the native toolkit for the OS, and only include those apps made specifically for elementary OS in their app store by default.
What many refer to as “Desktop Linux” is becomming easier to target as an app platform thanks to cross-project collaboration.
Flatpak is a containerized app packaging format that is widely used: Clear Linux, elementary OS, Endless OS, Fedora, KDE Neon, Linux Mint, Manjaro, Pop!_OS, PureOS, Red Hat Enterprise Linux, Solus, Zorin OS, and many more include Flatpak support out of the box.
Flathub is the defacto app store for all of Linux with thousands of apps, hundreds of apps verified by their own developers, and over a billion app installs. It’s a true community-led independent joint effort from GNOME, KDE, and independent contributors.
FreeDesktop.org specifications help ensure cross-compatibility between Linux-based desktops.
Portals provide apps well-defined, widely-supported APIs that work across OSes and desktop environments.
The Linux App Summit is an annual get-together with people working to create and grow a broad “Linux app ecosystem.”