bash -xv issue with stderr

[monochromec]

Configuration Information [Automatically generated, do not change]:
Machine: aarch64
OS: darwin24.0.0
Compiler: clang
Compilation CFLAGS: -DSSH_SOURCE_BASHRC 
-DDEFAULT_LOADABLE_BUILTINS_PATH='/opt/homebrew/Cellar/bash/5.2.37/lib/bash:/usr/local/lib/bash:/usr/lib/bash:/opt/local/lib/bash:/usr/pkg/lib/bash:/opt/pkg/lib/\
bash:.'
uname output: Darwin Christophs-MacBook-Air.local 24.1.0 Darwin Kernel Version 
24.1.0: Thu Oct 10 21:05:14 PDT 2024; root:xnu-11215.41.3~2/RELEASE_ARM64_T8103 
arm64
Machine Type: aarch64-apple-darwin24.0.0

Bash Version: 5.2
Patch Level: 37
Release Status: release

Description:
        Redirecting stderr to file causes output of bash -xv to be writte to 
file as well

Repeat-By:

test_bash.sh:
"
test_fun() {
    echo "to stderr" >&2
}

test_fun &>out
"
bash -xv test_bash.sh:
"
test_fun() {
    echo "to stderr" >&2
}

test_fun &>out
+ test_fun
"

out:
"
+ echo 'to stderr'
to stderr
"

Fix: