Same-type `agmsg spawn` (claude-code → claude-code) inherits the parent's session-identity env vars, breaks auth

[yktsnd]

I hit this building an autonomous dev pair: a Claude Code reviewer and a
Codex implementer, coordinated over agmsg. The setup itself runs as a
claude-code session, and it uses spawn to start both peers — including
a second, independent claude-code process for the reviewer. That
claude-code-spawning-claude-code step is what triggers the bug below.

This is a fairly specific use case, so if it's outside what spawn is
meant to support, feel free to close — just sharing the bug and fix in
case they're useful.

Symptom

Spawning a peer of the same CLI type you're already running as (e.g.
claude-code doing agmsg spawn claude-code <name>) leaves the child
showing a persistent Authentication error on every turn, even with
valid credentials.

Cause

spawn.sh's generated boot script execs the CLI without touching the
environment. tmux new-window/split-window copy the parent shell's
exported env verbatim, so a same-type child inherits the parent's
session-identity vars (CLAUDE_CODE_SESSION_ID, CLAUDECODE) and
mistakes the parent's session for its own:

export CLAUDE_CODE_SESSION_ID=outer-session-abc123
export CLAUDECODE=1
tmux new-session -d -s repro 'sleep 30'
tmux new-window -t repro -n child \
  'env | grep -E "^CLAUDE_CODE_SESSION_ID|^CLAUDECODE" > /tmp/child-env.txt'
cat /tmp/child-env.txt
# CLAUDE_CODE_SESSION_ID=outer-session-abc123
# CLAUDECODE=1

Related: #93 fixed a different flavor of the same "two processes, one
session_id" shape (resume, not spawn). #142 notes a process-tree fallback
in whoami that might mean env-var stripping alone isn't the full
picture.

Fix

type.conf's detect= already names the session-identity var(s) per
type — spawn.sh just never reads it. Unset them at the top of the
generated boot script:

--- a/scripts/spawn.sh
+++ b/scripts/spawn.sh
@@
 PROMPT_ARG="$(agmsg_type_get "$AGENT_TYPE" prompt_arg)"

+DETECT_VARS="$(agmsg_type_get "$AGENT_TYPE" detect)"
+[ "$DETECT_VARS" = "explicit" ] && DETECT_VARS=""
+
 # Extra CLI args for this type from the spawn options file (opt-in, see
@@
 {
   echo '#!/usr/bin/env bash'
   printf 'cd %q || exit 1\n' "$PROJECT"
+  if [ -n "$DETECT_VARS" ]; then
+    printf 'unset %s\n' "$DETECT_VARS"
+  fi
   if [ -n "$SPAWN_AGENT" ]; then

46/46 tests/test_spawn.bats pass with this applied (2 new cases);
confirmed they fail without it. Happy to PR if this fits, or adjust the
approach if you'd rather handle it differently.

agmsg 1.1.3 (main @ f665c1c), reproduced on Linux.