Backup TO URL WITH NOINIT fails because file already exists
Based on the documentation, it seems that is not supported.

Appending to existing backup blobs is not supported. Backups to an
existing blob can only be overwritten by using the WITH FORMAT option.
However, when using file-snapshot backups (using the WITH
FILE_SNAPSHOT argument), the WITH FORMAT argument is not permitted to
avoid leaving orphaned file-snapshots that were created with the
original file-snapshot backup.