Unable to start mysql

I already uninstall and reinstall mysql, but I am still getting error “ERROR 2002 (HY000): Can’t connect to local server through socket ‘/run/mysqld/mysqld.sock’ (2)” when trying to use it.

My journalctl -xeu mariadb.service shows this:

The job identifier is 1743.
jul 16 18:34:28 alberto-pc mariadbd[24722]: 2022-07-16 18:34:28 0 [Note] /usr/bin/mariadbd (server 10.8.3-MariaDB) starting as process 24722 ...
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Compressed tables use zlib 1.2.12
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Using transactional memory
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Number of transaction pools: 1
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Using crc32 + pclmulqdq instructions
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Using Linux native AIO
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Initializing buffer pool, total size = 128.000MiB, chunk size = 2.000MiB
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Completed initialization of buffer pool
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: File system buffers for log disabled (block size=4096 bytes)
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [ERROR] InnoDB: Upgrade after a crash is not supported. The redo log was created with MariaDB 10.5.8.
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [ERROR] InnoDB: Plugin initialization aborted with error Generic error
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] InnoDB: Starting shutdown...
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [ERROR] Plugin 'InnoDB' init function returned error.
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed.
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [Note] Zerofilling moved table:  './mysql/plugin'
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [ERROR] Unknown/unsupported storage engine: InnoDB
jul 16 18:34:29 alberto-pc mariadbd[24722]: 2022-07-16 18:34:29 0 [ERROR] Aborting
jul 16 18:34:29 alberto-pc systemd[1]: mariadb.service: Main process exited, code=exited, status=1/FAILURE
░░ Subject: Unit process exited
░░ Defined-By: systemd

░░ 
░░ An ExecStart= process belonging to unit mariadb.service has exited.
░░ 
░░ The process' exit code is 'exited' and its exit status is 1.
jul 16 18:34:29 alberto-pc systemd[1]: mariadb.service: Failed with result 'exit-code'.
░░ Subject: Unit failed
░░ Defined-By: systemd

░░ 
░░ The unit mariadb.service has entered the 'failed' state with result 'exit-code'.
jul 16 18:34:29 alberto-pc systemd[1]: Failed to start MariaDB 10.8.3 database server.
░░ Subject: A start job for unit mariadb.service has failed
░░ Defined-By: systemd

░░ 
░░ A start job for unit mariadb.service has finished with a failure.
░░ 
░░ The job identifier is 1743 and the job result is failed.

When trying to run mariabackup --prepare I get the same error: “ERROR 2002 (HY000): Can’t connect to local server through socket ‘/run/mysqld/mysqld.sock’ (2)”

The databases I had (nothing important) still remain in /var/lib/mysql and I already deleted the logs but still the same issue.

That else can I do to make my mysql run?

Read the docs - especially the part on installation, configuration and security