Automaion Api Random Deployment#instance errors

What happened?

We have a non-reproducable issue, which happens once a while every plan/up operation using automation api.

We have an inline program, which some times errors out with Trying to acquire Deployment#instance before 'run'.

This isn't really reproducable because it happens incosistantly.

Im really sure how to solve, this or even how to debug.
I wanted to see if anyout can provide insight on why this could happen, and if something could be attributing to this issue, especially it being inconsistent.

Example

The only special or "unique" thing im doing which could be a cause for the issue, is that my first defined resource which is seeing this error is a stack reference, seeing as a StackReference is just a CustomResource, I don't think this is relevant.

Output of pulumi about

CLI
Version 3.212.0
Go Version go1.25.5
Go Compiler gc

Host
OS nixos
Version 26.05 (Yarara)
Arch x86_64

Pulumi locates its logs in /tmp by default

Additional context

No response

Contributing

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To contribute a fix for this issue, leave a comment (and link to your pull request, if you've opened one already).

Start with the Automation API deployment lifecycle around the reported Deployment#instance error, using the inline program and StackReference case described in the issue. Reproduce or instrument the operation in the supplied Pulumi 3.212.0, Go 1.25.5, and NixOS environment; done means the inconsistent failure has a confirmed cause and a documented fix or diagnostic path.