kern.log and syslog grow 40+ GB in few minutes

By the way the bash script is wrong. Should be:

#!/bin/bash
for log in test; do
  echo "${log} :"
  sed -e 's/[[^]]+]//' -e 's/.*[0-9]{2}:[0-9]{2}:[0-9]{2}//' ${log} 
  | sort | uniq -c | sort -hr | head -10
done

I tested it, but have no idea what test in your case is.

List below file:

cat /etc/logrotate.d/rsyslog

should contain this:

/var/log/syslog
{
    rotate 7
    daily
    missingok
    notifempty
    delaycompress
    compress
    postrotate
            /usr/lib/rsyslog/rsyslog-rotate
    endscript
}

/var/log/mail.info
/var/log/mail.warn
/var/log/mail.err
/var/log/mail.log
/var/log/daemon.log
/var/log/kern.log
/var/log/auth.log
/var/log/user.log
/var/log/lpr.log
/var/log/cron.log
/var/log/debug
/var/log/messages
{
    rotate 4
    weekly
    missingok
    notifempty
    compress
    delaycompress
    sharedscripts
    postrotate
            /usr/lib/rsyslog/rsyslog-rotate
    endscript
}

If it does not contain the above , edit it and replace

sudo nano /etc/logrotate.d/rsyslog

Then force the logrotate manually:

sudo logrotate --force  /etc/logrotate.d/rsyslog

If it will show similar error:

error: skipping "/var/log/syslog" because parent directory has insecure permissions (It's world writable or writable by group which is not "root") Set "su" directive in config file to tell logrotate which user/group should be used for rotation.

Then type in terminal:

sudo chmod 755 /var/log/ && sudo chown root:root /var/log/
sudo chmod 755 /var && sudo chown root:root /var
sudo logrotate --force  /etc/logrotate.d/rsyslog

How to upgrade Elementary OS to the 5.7.0 kernel.

Install necessary packages

sudo apt-get install build-essential libncurses-dev bison flex libssl-dev libelf-dev

To check hardware

sudo lspci

To check missing firmware

sudo update-initramfs -u

This step is important, because it shows missing firmware.

Make directories for firmware

mkdir /home/username/Downloads/kernel
mkdir /home/username/Downloads/amdgpu
mkdir /home/username/Downloads/i915
mkdir /home/username/Downloads/rtl

To get rid of missing firmware errors for amdgpu

cd /home/username/Downloads/amdgpu
wget https://github.com/M-Bab/linux-kernel-amdgpu-binaries/files/4124959/firmware-radeon-ucode-rock_2.110_all.deb.zip
unzip firmware-radeon-ucode-rock_2.110_all.deb.zip
sudo dpkg -i firmware-radeon-ucode-rock_2.110_all.deb

Or use eddy to install this deb

Source: https://github.com/M-Bab/linux-kernel-amdgpu-binaries/issues/82

To get rid of missing firmware errors for i915

cd /home/username/Downloads/i915
git clone https://git.kernel.org/pub/scm/linux/kernel/git/firmware/linux-firmware.git
sudo cp -R /linux-firmware/i915/* /lib/firmware/i915/

To get rid of missing firmware errors for rtl (Realtek LAN and Wi-Fi adapters in my DELL)

cd /home/username/Downloads/rtl
wget https://git.kernel.org/pub/scm/linux/kernel/git/firmware/linux-firmware.git/plain/rtl_nic/rtl8168fp-3.fw
wget https://git.kernel.org/pub/scm/linux/kernel/git/firmware/linux-firmware.git/plain/rtl_nic/rtl8125a-3.fw
sudo cp rtl8168fp-3.fw /lib/firmware/rtl_nic 
sudo cp rtl8125a-3.fw /lib/firmware/rtl_nic

Download kernel 5.7.0

cd /home/username/Downloads/kernel
wget https://cdn.kernel.org/pub/linux/kernel/v5.x/linux-5.7.tar.xz
tar -xf linux-5.7.tar.xz
cd linux-5.7
cp -v /boot/config-$(uname -r) .config
make menuconfig 

save config and then exit.

Use 4 core/thread - if your processor have 4 cores

make -j 4

Use 8 core/thread - if your processor have 8 cores

make -j 8

Then type below commands:

sudo make modules_install 
sudo make install 
sudo update-initramfs -c -k 5.7.0

ignore these errors below, just because those three bin files are not made yet W: Possible missing firmware /lib/firmware/amdgpu/navi12_ta.bin for module amdgpu W: Possible missing firmware /lib/firmware/amdgpu/navi10_mes.bin for module amdgpu W: Possible missing firmware /lib/firmware/amdgpu/navi12_dmcu.bin for module amdgpu

Type in terminal:

sudo update-grub
sudo reboot
uname -mrs

To check errors after reboot:

sudo journalctl -b
sudo dmesg

It looks like you are using hwe kernel. Can you remove it together with headers and then update the grub and also initramfs?