Not able to regulate/auto grow tempdb size
As Tibor mentioned in the comments, add your SQL Server Service account to the Perform volume maintenance tasks local security policy so it can perform Instant File Initialization.  I personally don't feel that alone will solve your problem as I suspect you may be running into the byproduct of thin provisioned disk.  A nice definition being as follows:


  A thin-provisioned virtual disk consumes only the space that it needs initially, and grows with time according to demand.


First, are these servers VMs?  If so, is your infrastructure team presenting VM disk that has been thin provisioned?

Alternatively is the SAN presenting thin provisioned disk to the VM or physical hosts (in the event they are not VMs)?

What can happen with thin provisioned disk is that when additional space is requested to be allocated, and the underlying disk pool/group is over-allocated, you'll run into errors similar to what you're seeing as there's no more actual storage available.  From the OS perspective, the disk has plenty of free space to expand into, but you get these random errors that make no sense.  Databases tend to suffer most from thin-provisioning as they often request resources in large quantities and need said resources quickly, and thin-provisioning mechanisms are built for slow and steady rather than varied and rapid.

It is pretty easy to identify if this is your issue or not as you only need to reach out to both your VM admins and your storage admins.  Ask if any of the underlying disk the TempDB (or any other database) files are on are thin provisioned, and if so how much actual space is available to use.  I've run into scenarios where the OS showed I had a 1 TB drive, but in actuality, I was limited to significantly less space as the underlying disk pool didn't have enough actual storage to honor the extra space the OS was told it has.

I hate when resources are thin provisioned (especially when this happens with memory) because you're not working with all the resources you've been promised.  It's basically like telling your kids they can spend $100 but you only have $80 available and you just hope they are fiscally responsible.  I've yet to work in an environment where thin provisioning doesn't eventually cause issues.  Database Servers should be built for usage spikes rather than averages, and infrastructure admins hate seeing idle resources so many times they offer thin-provisioning as a compromised approach.