My question is whether I need to add a new data disk to install Parse
Server, or can I do it having the OS disk only?
We'd better add a new data disk to host application or data.
By default, Linux VM OS disk size is 30 GB, maximum capacity of 2048 GB.
If you just want to create a test lab, I think you can host your application or data on OS disk.
If not a test lab, I think we should create a new disk to host Application or data. Each data disk has a maximum capacity of 4095 GB, add new data disk, we can have more IO.
You add extra disks as needed per your space and IOps requirements. Each disk has a performance target of 500 IOps for Standard Storage and up to 5000 IOps per disk for Premium Storage.
More information about Azure VM IOps, please refer to this blog.
Also if you want to add a new data disk, please refer to this link.