Are you using the installed version or a live usb?

Installed version

did you tried to use alsamixer (alsa-utils)

No, I didn't. Please elaborate.

in alsamixer you can manage volume of all speakers mics that you have besides try using pavucontrol package to set volume on system sound and others or maybe your problem is in drivers ?

Volume control works fine, I think the problem is not in the drivers but in the persistence of the set values, i.e it's reset to the default values after logout/login rather than being saved and stay persistent after logout/login (which I believe is the desired behavior - all other OS I've worked with have persistent volume)

How are you changing the volume, and what desktop is this in?

Volume bar at the top right or via keyboard Fn keys. I use Xfce desktop env.

Have you tried moving your ~/.cache folder to a different name and see if that helps at all? Or possibly run pavucontrol from a terminal and see if it spits anything out when you try to change the volume?

Actually - had another thought - does your root user have a ~/.config/pulse directory?

I did what steev suggested, got this:
pavucontrol doesn't spit anything, I can change the volume as expected.
If pavucontrol is open - when I log out and log back in - the volume is persistent (stays the same as was configured before the log-out).
If I close pavucontrol - when I log out and log back in - the volume is set to default value.
I do have ~/.config/pulse dir with some backup files (.tdb) and some default configs.

When you say you do have ~/.config/pulse - are you saying for root? or just for your normal user? If root, can you try removing root's copy of ~/.config/pulse and then see if the changes stay persistent?

Oh, you meant the actual root user?
root user doesn't have this folder, only my user (which has root privileges)

i have almost same problem instead of logging out when i change song on youtube volume in pavucontrol changes everytime

Can you both try moving the ~/.config/pulse directory out of the way? Also, to be sure, can you please give us the output of dpkg -l | grep pulse

mine output of dpkg -l | grep pulse :
ii gstreamer1.0-pulseaudio:amd64 1.20.3-1 amd64 GStreamer plugin for PulseAudio (transitional package)
ii libkf5pulseaudioqt3:amd64 1.3-2 amd64 Pulseaudio bindings library for Qt
ii libpulse-mainloop-glib0:amd64 15.0+dfsg1-4+b1 amd64 PulseAudio client libraries (glib support)
ii libpulse0:amd64 15.0+dfsg1-4+b1 amd64 PulseAudio client libraries
ii libpulsedsp:amd64 15.0+dfsg1-4+b1 amd64 PulseAudio OSS pre-load library
ii pulseaudio 15.0+dfsg1-4+b1 amd64 PulseAudio sound server
ii pulseaudio-module-bluetooth 15.0+dfsg1-4+b1 amd64 Bluetooth module for PulseAudio sound server
ii pulseaudio-utils 15.0+dfsg1-4+b1 amd64 Command line tools for the PulseAudio sound server

Moving the folder ~/.config/pulse didn't help.

dpkg output:

└─$ dpkg -l | grep pulse
ii libpulse-mainloop-glib0:amd64 15.0+dfsg1-4+b1 amd64 PulseAudio client libraries (glib support)
ii libpulse0:amd64 15.0+dfsg1-4+b1 amd64 PulseAudio client libraries
ii libpulsedsp:amd64 15.0+dfsg1-4+b1 amd64 PulseAudio OSS pre-load library
ii pulseaudio 15.0+dfsg1-4+b1 amd64 PulseAudio sound server
ii pulseaudio-module-bluetooth 15.0+dfsg1-4+b1 amd64 Bluetooth module for PulseAudio sound server
ii pulseaudio-utils 15.0+dfsg1-4+b1 amd64 Command line tools for the PulseAudio sound server
ii xfce4-pulseaudio-plugin:amd64 0.4.3-1 amd64 Xfce4 panel plugin to control pulseaudio

Can't reproduce in QEMU/KVM, sorry.

This report has been filed against an old version of Kali. We will be closing this ticket due to inactivity.

Please could you see if you are able to replicate this issue with the latest version of Kali Linux (https://www.kali.org/get-kali/)?

If you are still facing the same problem, feel free to re-open the ticket. If you choose to do this, could you provide more information to the issue you are facing, and also give information about your setup?
For more information, please read: https://www.kali.org/docs/community/submitting-issues-kali-bug-tracker/