Add deprecation notice and documentation

[swang392]

What does this PR do?

Add deprecation logs when runProcessChecksInCoreAgent is enabled and centralized documentation for deprecated configs.

Motivation

Deprecation process for #2178

Additional Notes

Anything else we should know when reviewing?

Minimum Agent Versions

Are there minimum versions of the Datadog Agent and/or Cluster Agent required?

• Agent: vX.Y.Z
• Cluster Agent: vX.Y.Z

Describe your test plan

• build and deploy custom operator image
• apply a DDA config with runProcessChecksInCoreAgent enabled
• look into operator logs, verify that a deprecation notice error log is there:

{"level":"ERROR","ts":"2025-09-22T17:07:26.393Z","logger":"controllers.DatadogAgent","msg":"DEPRECATION WARNING: The 'runProcessChecksInCoreAgent' configuration will be deprecated in v1.21. This field can be safely removed with no behavior change.","datadogagent":{"name":"datadog","namespace":"system"},"stacktrace":"github.com/DataDog/datadog-operator/internal/controller/datadogagent.(*Reconciler).internalReconcileV2\n\t/workspace/internal/controller/datadogagent/controller_reconcile_v2.go:45\ngithub.com/DataDog/datadog-operator/internal/controller/datadogagent.(*Reconciler).Reconcile\n\t/workspace/internal/controller/datadogagent/controller.go:106\ngithub.com/DataDog/datadog-operator/internal/controller.(*DatadogAgentReconciler).Reconcile\n\t/workspace/internal/controller/datadogagent_controller.go:188\nsigs.k8s.io/controller-runtime/pkg/reconcile.(*objectReconcilerAdapter[...]).Reconcile\n\t/go/pkg/mod/sigs.k8s.io/[email protected]/pkg/reconcile/reconcile.go:154\nsigs.k8s.io/controller-runtime/pkg/internal/controller.(*Controller[...]).Reconcile\n\t/go/pkg/mod/sigs.k8s.io/[email protected]/pkg/internal/controller/controller.go:119\nsigs.k8s.io/controller-runtime/pkg/internal/controller.(*Controller[...]).reconcileHandler\n\t/go/pkg/mod/sigs.k8s.io/[email protected]/pkg/internal/controller/controller.go:334\nsigs.k8s.io/controller-runtime/pkg/internal/controller.(*Controller[...]).processNextWorkItem\n\t/go/pkg/mod/sigs.k8s.io/[email protected]/pkg/internal/controller/controller.go:294\nsigs.k8s.io/controller-runtime/pkg/internal/controller.(*Controller[...]).Start.func2.2\n\t/go/pkg/mod/sigs.k8s.io/[email protected]/pkg/internal/controller/controller.go:255"}

Checklist

• PR has at least one valid label: bug, enhancement, refactoring, documentation, tooling, and/or dependencies
• PR has a milestone or the qa/skip-qa label

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 38.83%. Comparing base (7e19847) to head (7de9493).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2195   +/-   ##
=======================================
  Coverage   38.82%   38.83%           
=======================================
  Files         254      254           
  Lines       26097    26100    +3     
=======================================
+ Hits        10132    10135    +3     
  Misses      15356    15356           
  Partials      609      609           

Flag	Coverage Δ
unittests	38.83% <100.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...controller/datadogagent/controller_reconcile_v2.go	58.62% <100.00%> (+0.54%)	⬆️

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