Is it possible to downgrade kernel on Ubuntu 21.10 to something lower then 5.13x?

Solution 1:

• You can pick all available kernels at the grub prompt.
• you can set grub to use a specific kernel if available
• you can install more kernels.

The concept of "downgrading" does not apply here (you do not replace a kernel with another; you add kernels or delete kernels from your system (when you logged into the kernel you want to use)).

The tool you mentioned is probably UKUU (Ubuntu Kernel Update Utility) but is no longer FREE so got removed. Have a look at mainline (that is a new version of UKUU):

Features

• Fetches the list of available kernels from the Ubuntu Mainline PPA
• Optionally watches and displays notifications when a new kernel update is available
• Downloads and installs packages automatically
• Display available and installed kernels conveniently
• Install/Uninstall kernels from gui
• For each kernel, the related packages (headers & modules) are installed or uninstalled at the same time

Installation using PPA

sudo add-apt-repository ppa:cappelikan/ppa
sudo apt update
sudo apt install mainline