The previous `_build_runtime_bin_prefix()` skipped candidate dirs that
were already present in the LAUNCHER process's \$PATH. This is wrong:
the tmux pane inherits the tmux SERVER environment, not the launcher's
env. A dir on the launcher's \$PATH may be absent from the server env,
so the prefix could come back empty and the pane would fail with
'command not found'.
Remove the `case ":${PATH}:"` check that tested against the live launcher
PATH. Keep the existence check (`[ -d "$dir" ]`) and the dedup-within-
the-constructed-prefix guard. The pane command's `export PATH="<prefix>:${PATH}"`
harmlessly absorbs any overlap with the server PATH.
Add test 5 to test-start-agent-session.sh: sets FAKE_RUNTIME_BIN5 on the
launcher's \$PATH and asserts it still appears in the generated pane PATH
export — directly guarding this regression.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01RMoEx7hfdFGjUiCHuN1RRi
a2b11118e3