@sergeyprotserovca I work for SHARCNET (one of the Canadian HPC providers/alliance members). One of my colleagues pointed me to your post.
You really don’t want the nix unpacked under your home directory. Not only will this kill your file-count quota, it gives very bad performance. The reason is HOME is a shared filesystem and meta-data operations (opening files, closing files, list files, etc.) all have to be globally synchronization across the entire cluster to ensure a consistent filesystem. This makes all directory operations a real bottleneck (creating files, opening files, deleting files, listing files, etc.). Only reading and writing to files once they are open is fast, so you want to work with a few large files opened once, not many small files with lots of opening and closing.
One option is to stick the nix store in a filesystem image (a single large file) and mount that read only (after you have set it up) with apptainer. A potentially better option is to just keep a tarball of your store in your directory and unpack it to local storage on each machine you want to run on. I’ll post a follow up message with an example of how this can be done.
With regard to accessing your local store, nix needs to mount it as /nix. This requires nix to create a new mount namespace, and nix can then only pass this onto decedent processes. It cannot force it onto its parent process. So a new sub-shell is the only option (see here for the docs about how a local store works).
I would also personally recommend using the nix shell command to spawn a new sub-shell with /nix mounted and PATH extended and not nix develop unless you actually want a development environment.
nix shell nixpkgs#yazi nixpkgs#btop
Not sure I follow exactly what your doing/what is going on with your locales, but possibly you should be using C.UTF-8 as this is the most basic locale. Currently there is a regression on the latest nibi (the supercomputer SHARCNET manages) image so LANG is no longer set. This results is come programs, like btop no longer running. You can work around this by manually setting it yourself export LANG=C.UTF-8.
I would also note, that the SHARCNET systems (formerly graham and now nibi) do have a global nix install. The new nibi one doesn’t yet have a user accessibly nix-daemon, but that is on my todo list. It doesn’t seem likely though that the non-SHARCNET systems (fir, trillium, rorqual, etc.) will have a global nix install anytime soon. So you still need to use the local install method on them.