I think you can install fish from the discover store, which will persist between updates. You may need to also update its permissions through flatseal so that it has full file system access.

Some other options for packages are to install them through nix or distrobox. There’s also a set of commands for installing a package locally, but I would have to look it up. It involves setting a temporary cache directory, downloading the package there without installing it, and then installing the contents of cache to a folder in user-space.