Can't run `nix-channel --update` in `nixos-enter` session

I’m having trouble doing things from within nixos-enter. Though to be fair to nixos-enter, all the same issues appear when chrooting manually.

In particular,

iso$ sudo nixos-enter
chroot-root# su skainswo
chroot-skainswo$ nix-channel --update
error: could not set permissions on '/nix/var/nix/profiles/per-user' to 755: Operation not permitted

Does any know what’s going wrong here? I’d like to install home-manager (following the directions here) in the /mnt NixOS system when booting from the ISO.

Seemingly related: error: could not set permissions on '/nix/var/nix/profiles/per-user' to 755: Operation not permitted · Issue #3435 · NixOS/nix · GitHub

I haven’t used nixos-enter so I’m not sure about the underlying issue, but I don’t think it is directly related to #3435 (the message is the same, but the reports in 3435 were all about nix on macOS).