Can I download Linux software once and install it fully offline?

AppImage is probably the closest fit. It usually bundles the application and many of its dependencies into one file, so you can save it and run it without a separate installation.

It is not a guarantee that every AppImage will work on every Linux system. Keep a copy that matches your processor architecture and test it on the target system while you can. Also, not every application is available as an AppImage.

Regular distribution packages can work offline too, but a single package file may not contain everything it needs. You would need to download the application and all missing dependency packages for the target distribution and architecture, then transfer them together.

For a larger collection, an offline copy of a distribution repository is another option. That's more work and takes more space, but it gives the package manager a local source for dependencies.

Flatpak is another option, but don't assume the application file alone contains everything. Flatpak apps can depend on separate runtimes, so preserve the required runtime as well and test the offline installation.

Some projects also distribute self-contained Linux archives directly. Blender is one example. Check what the project provides and keep the downloaded archive, rather than assuming every installer will bundle all its dependencies.

One distinction: installing offline and using offline are separate questions. Many programs work without a connection once installed, but that doesn't mean their original installer included everything. Some software can also need an online service for particular features.