You can install packages in immutable distros. It's just not as easy and recommended as a last resort.
With Universal Blue (Bazzite, Bluefin, Aurora) you can install packages with "layering". It's basically modifying the image by adding packages on top of what is shipped by the distro, and those packages get added each time the image is updated.
The better, more involved solution is to create your own image from the base image. That gives you a lot more control. You can even remove packages from the base image.