My VEEAM community is on Windows 10 now. I want to upgrade it. Does VEEAM backup support Ubuntu/Mariadb

It should support Ubuntu, check here for the requirements - System Requirements - User Guide for VMware vSphere

Community Edition of VBR is Windows only. Version 13 has released with an early preview of a Linux-based appliance but it is installed from a Veeam provided ISO and I believe it is Rocky/RHEL based. In order to use this “Veeam Software Appliance” you need an NFR key or paid license. For the VBR database your options on Windows are Microsoft SQL or PostgreSQL. The software appliance deploys and uses PostgreSQL as part of the installation.

If you are talking backing up a machine and not running VBR, Ubuntu is supported for agents.

Ubuntu / MariaDB as the backup server.   

​@SCSIraidGURU do you want to use MariaDB as a Veeam Data Base server instead of Postgres or MSSQL? 

I used Postgres in the past.   It would crash when the Linux upgraded.  No matter which flavor: Redhat or Debian.   MSSQL is Microsoft.   I use MariaDB on my Ubuntu web server.   I can update the Ubuntu server and reboot it.  MariaDB stays stable.  They have good LTSR support.   I am on MariaDB 11.4.8.  Support through 2029 for community support.  PHPMyAdmin works great with it.  

Unfortunately you cannot run Veeam Backup & Replication on Ubuntu. Also MariaDB isn't a supported database. You need to stay on Windows and can decide whether you use MS SQL or PostgreSQL as the database.

The Veeam Software appliance on the other hand is pre-packed and is running Linux in the backend. Unfortunately as ​@JonahMay already said it's not available as Community Edition but maybe you can request a NFR.