Note: If your Hyper-V host is running Windows Server 2016 (or newer) and your SQL VM is running on a Windows Server 2012R2 (or older) operating system, please note that there is a confirmed Microsoft bug.
A fix has been released by Microsoft in March 2021 for this issue. The KB article can be found here.
When running SQL inside a guest VM, the Microsoft SQL Transaction Logs are not being truncated after a VM backup succeeds.
Since VM Backup uses Microsoft Shadow Copy tasks to backup VMs, it will only trigger a Database Backup, not a Database Log Backup, thus transaction logs will only be truncated when VM Backup runs a backup if you select the Simple Recovery Model for your SQL databases.
More information on SQL recovery models can be found here: https://msdn.microsoft.com/en-us/library/ms189275.aspx
Simple recovery model
Under a Simple Recovery Model, SQL will truncate the transaction logs when a Shadow copy is taken. This happens when VM Backup requests a Shadow Copy from the MS Hyper-V VSS writer, this then cascades the shadow copy task into the guest VM and the MS SQL VSS writer will kick off a Database backup, This process will truncate the transaction logs, assuming of course that the SQL VSS writer is installed and enabled.
Full or Bulk Logged recovery model
Under the Full or Bulk Recovery Model the transaction logs are not truncated until a Database Log Backup has been completed. In VM Backup, a backup is not considered a Database Log Backup. If the Full or Bulk Recovery Model is required, using the Microsoft SQL Management Studio to schedule a Transaction Log Backup Task will be required to maintain the Transaction Log size.
Note: This is not a best practice on how to set up a SQL server but an explanation of how VM Backup interacts with SQL and its different recovery models.