in case of Managed Instance (Azure SQL DB) you have no control over the underlying instance.
All you can do is to get understanding how big tempdb can be according to your service tier (either DTU, vCore, others).
To prevent filling up the tempdb, you can control its size during data upload and/or setup alerts based on current tempdb size.
when I started working with Azure SQL DB 8 months ago, it became clear that a lot of things are hidden and not available in portal.azure.com interface.
So, I started creating SSMS dashboards (custom reports) which helped me and my colleagues to get answers on the frequent practical questions like "what is running now, how much ram is available, why my query is not progressing, what was running today early in the morning", etc.
Dashboards are available here: