Running bazel in a subshell causes subshell to hang

### Description of the bug:

This hangs. This only ends after I manually shutdown the server from another terminal window.

```
bazel shutdown;
( ( tools/bazel version ) | cat ) 3>&1 1>&2 2>&3 | cat
```

This only happens when the bazel server is started within a subshell within a subshell (hence the `bazel shutdown` at the beginning). I checked the process tree and the bazel server is attached to `systemd`, but the second `cat` still waits for the server to shutdown.

### Which category does this issue belong to?

Local Execution

### What's the simplest, easiest way to reproduce this bug? Please provide a minimal example if possible.

```
bazel shutdown;
( ( tools/bazel version ) | cat ) 3>&1 1>&2 2>&3 | cat
```

OR, here's a simplified version of my original build command that causes the issue. I am trying to `tee` stdout and stderr to different files.

```
( ( bazel build //foo:bar ) | tee stdout.txt ) 3>&1 1>&2 2>&3 | tee stderr.txt
```

### Which operating system are you running Bazel on?

Linux

### What is the output of `bazel info release`?

development version

### If `bazel info release` returns `development version` or `(@non-git)`, tell us how you built Bazel.

From https://cs.android.com/android/kernel/superproject/+/common-android-mainline:prebuilts/bazel/linux-x86_64/

### What's the output of `git remote get-url origin; git rev-parse master; git rev-parse HEAD` ?

```text
N/A
```

### Is this a regression? If yes, please try to identify the Bazel commit where the bug was introduced.

Probably not

### Have you found anything relevant by searching the web?

_No response_

### Any other information, logs, or outputs that you want to share?

Workaround is to run `bazel version > /dev/null` right after `bazel shutdown` to start the bazel server not in a subshell.

Reproduce the issue on Linux using the nested `tools/bazel version` and `bazel build //foo:bar` pipeline commands, beginning with `bazel shutdown`. Trace the Bazel server startup and shutdown behavior in these subshells; done means the pipeline's final `cat` exits without a manual server shutdown, while preserving the separate stdout and stderr behavior shown.

Written by the indexing model from the issue text.