mysql.service failure and can't connect to mysql.sock file - Debian 12 VPS

[sasa predic]

Hello,
I hope I ask question in the right place and that there will be some expert who can help.

I installed yesterday Debian 12 on new VPS, then after php and apache I wanted to install mysql but I got problem, today I can not even start mysql, yesterday ir worked as process but not as port 3306.

let's start description of problem:

I downloaded with wget mysql-apt-config_0.8.33-1_all.deb
I installed this package and mysql server, I think I chose option 8.4.0, but it was not possible to use mysql because it was written there is already running mysql although command "netstat -tpln" showed me there is NO 3306 port connection, there was ssh and apache connection but not mysql. when I tried HTOP command, I saw mysql processes. In any case, mysql start restart and stop didn't help anything. I could not use mysql in my new VPS.

it was last night, today, I can not even start mysql server.
sudo systemctl start mysql
Job for mysql.service failed because the control process exited with error code.
See "systemctl status mysql.service" and "journalctl -xeu mysql.service" for details.

journalctl -xeu mysql.service
An ExecStart= process belonging to unit mysql.service has exited.
systemd[1]: mysql.service: Failed with result 'exit-code'.
systemd[1]: mysql.service: Main process exited, code=exited, status=1/FAILURE
systemd[1]: Failed to start mysql.service - MySQL Community Server.

here is result from mysql error.log file:
[Server] /usr/sbin/mysqld (mysqld 8.0.40) starting as process 21134
[System] [MY-013576] [InnoDB] InnoDB initialization has started.
[ERROR] [MY-014061] [InnoDB] Invalid MySQL server downgrade: Cannot downgrade from 80403 to 80040. Downgrade is only permitted between patch releases.
mysqld: Can't open file: 'mysql.ibd' (errno: 0 - )
[ERROR] [MY-010334] [Server] Failed to initialize DD Storage Engine
[ERROR] [MY-010020] [Server] Data Dictionary initialization failed.
[ERROR] [MY-010119] [Server] Aborting
[System] [MY-010910] [Server] /usr/sbin/mysqld: Shutdown complete (mysqld 8.0.40) MySQL Community Server - GPL.

after that I tried to add client section in my.cnf file, but I get error can't connect with sock file:
mysql -u root -h localhost -p
Enter password:
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)

I tried mysql and mysqld folder in my.cnf file but it is the same error.

cat /etc/mysql/my.cnf

!includedir /etc/mysql/conf.d/
!includedir /etc/mysql/mysql.conf.d/
[client]
password = ***secret***
port = 3306
host = 127.0.0.1
#socket = /var/lib/mysql/mysql.sock
socket=/var/run/mysqld/mysql.sock

yesterday i tried also to remove and purge and install mysql again, but I get again the same error.
any advice from anybody?