How to print logs to serial port without specifying ‘console’ in Linux?

I am working on an embedded Linux system (5.19.10), and I am using busybox as the main part of file system.

Now I am trying to run a test which should output logs to the serial port (ttyS0). But I did NOT configure console in the kernel command line.

The /etc/inittab is as follows,

# now run any rc scripts
::sysinit:/etc/init.d/rcS

# Put a getty on the serial port
#::respawn:/sbin/getty -L ttyS1 115200 vt100
#no login
::respawn:-/bin/sh

# Stuff to do for the 3-finger salute
::ctrlaltdel:/sbin/reboot

# Stuff to do before rebooting
null::shutdown:/etc/init.d/rcK
null::shutdown:/bin/umount -a -r
null::shutdown:/sbin/swapoff -a

I changed the /etc/profile as follows,

export PATH="/bin:/sbin:/usr/bin:/usr/sbin"
stty -F /dev/ttyS0 speed 38400
setconsole /dev/ttyS0
echo "Hello world" > /dev/ttyS0
/home/test/test_app 2>&1 &

When system booted up, I can see Hello world in the serial port. But I cannot see the shell prompt or the logs from the test_app.

I think the system console is NOT being configured correctly in this case.
So, I am wondering is there any gental way to set the system console in my own script (e.g. /etc/init.d/rcS or /etc/profile) without using getty or console=XXX and make the log output to the serial expected console??