[Bug]: `atuin pty-proxy init` exports `SHELL=zsh` instead of the spawned shell path

[hangrymuppet]

What did you expect to happen?

When Atuin pty-proxy launches a proxied zsh session, $SHELL should remain an executable path for the shell that launched Atuin.

For example, on a macOS system whose terminal launches the login shell as /bin/zsh, the proxied session should keep:

SHELL=/bin/zsh

This matters because many tools correctly expect $SHELL to refer to an executable path.

What happened?

atuin pty-proxy init can launch the proxied zsh with:

SHELL=zsh

Atuin doctor output

{
  "atuin": {
    "version": "18.17.0",
    "commit": "",
    "sync": {
      "auth_state": "Hub (legacy token — run 'atuin login' to upgrade)",
      "records": true,
      "auto_sync": true,
      "last_sync": "REDACTED"
    },
    "sqlite_version": "3.46.0",
    "daemon_enabled": true
  },
  "shell": {
    "name": "zsh",
    "default": "zsh",
    "plugins": [
      "atuin"
    ],
    "preexec": "built-in"
  },
  "system": {
    "os": "Darwin",
    "arch": "arm64",
    "version": "26.5.2",
    "disks": [
      {
        "name": "Macintosh HD",
        "filesystem": "apfs"
      },
      {
        "name": "Macintosh HD",
        "filesystem": "apfs"
      }
    ]
  }
}

Shell setup

The shell startup runs Atuin pty-proxy early:

if [[ "$-" == *i* ]] && command -v atuin >/dev/null 2>&1; then
  eval "$(atuin pty-proxy init)"
fi

The generated zsh init code currently uses ZSH_ARGZERO directly after
stripping a leading login-shell dash:

_atuin_pty_proxy_zsh="${ZSH_ARGZERO:-$(command -v zsh)}"
exec atuin pty-proxy --shell "${_atuin_pty_proxy_zsh#-}"

In the affected proxied session:

ATUIN_PTY_PROXY_ACTIVE=1
ATUIN_PTY_PROXY_SOCKET=/var/folders/.../T/atuin-pty-proxy-70454.sock
SHELL=zsh                    # <-- not an executable path
argv0=zsh
ZSH_ARGZERO=zsh
command -v zsh=/opt/homebrew/bin/zsh
ZSH_VERSION=5.9.1            # PATH shell version, not the launch shell version
SHELL is not executable      # [ -x "$SHELL" ] returns false

With Atuin pty-proxy disabled in the same terminal environment:

SHELL=/bin/zsh               # <-- the expected executable path
argv0=-zsh
ZSH_ARGZERO=-zsh
command -v zsh=/opt/homebrew/bin/zsh
ZSH_VERSION=5.9              # launch shell version
SHELL is executable          # [ -x "$SHELL" ] returns true

Snippet to produce the above output:

env | rg '^(SHELL|ATUIN_PTY_PROXY_ACTIVE|ATUIN_PTY_PROXY_SOCKET)='
printf 'argv0=%s\n' "$0"
printf 'ZSH_ARGZERO=%s\n' "$ZSH_ARGZERO"
printf 'command -v zsh=%s\n' "$(command -v zsh)"
printf 'ZSH_VERSION=%s\n' "$ZSH_VERSION"
[[ -x "$SHELL" ]] && echo "SHELL is executable" || echo "SHELL is not executable"

Why this appears to be a regression

PR #3548 intentionally changed the pty-proxy runtime to set $SHELL to the
spawned shell:

cmd.env("SHELL", path);

That intent makes sense, but the generated zsh init path can pass a non-path
value from ZSH_ARGZERO:

atuin pty-proxy --shell zsh

Before #3548, this bad --shell zsh value may not have overwritten an inherited
absolute $SHELL. After #3548, it becomes visible as SHELL=zsh.

Code of Conduct

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[hangrymuppet]

I am working on a PR