Backing up SQL Server Express Edition on a VPS
Your best bet would be to use ola Hallengren's utilities

https://ola.hallengren.com/

from the faq

How do I get started with the SQL Server Maintenance Solution on SQL Server Express?

SQL Server Express has no SQL Server Agent. Therefore, the execution of the stored procedures must be scheduled by using cmd files and Windows Scheduled Tasks. Follow these steps.

    Download MaintenanceSolution.sql.
    Execute MaintenanceSolution.sql. This script creates the stored procedures that you need.
    Create cmd files to execute the stored procedures; for example:
    sqlcmd -E -S .\SQLEXPRESS -d master -Q "EXECUTE dbo.DatabaseBackup @Databases = 'USER_DATABASES', @Directory = N'C:\Backup', @BackupType = 'FULL'" -b -o C:\Log\DatabaseBackup.txt
    In Windows Scheduled Tasks, create tasks to call the cmd files.
    Schedule the tasks.
    Start the tasks and verify that they are completing successfully.


Another option would be to use the DBATools Powershell module and create and schedule powershell scripts.