Use a fresh context for automation api runs

[Frassle]

Description

Looks like this should help with some async context tracking for python. We make a fresh context for running the Automation API program and so don't need to reset globals on exit.

We also fix configure to set the context variables rather than overwriting the SETTINGS object itself which is just a plain global.

Checklist

• I have run make tidy to update any new dependencies
• I have run make lint to verify my code passes the lint check
  • I have formatted my code using gofumpt

• I have added tests that prove my fix is effective or that my feature works

• I have run make changelog and committed the changelog/pending/<file> documenting my change

• Yes, there are changes in this PR that warrants bumping the Pulumi Cloud API version

[pulumi-bot]

Changelog

[uncommitted] (2024-04-26)

Bug Fixes

• [auto/python] Ensure async context is not shared between multiple programs
  #16063