fix(mixin): use withMixin in Stack to set mixin metadata in its constructs

[Abogical]

Reason for this change

Previously, if a stack has a mixin applied (using with), the stack's child constructs will not have its mixin metadata set. Stack used applyTo directly instead of applyMixin which adds the metadata via addMetadata in https://github.com/aws/aws-cdk/blob/main/packages/aws-cdk-lib/core/lib/mixins/private/mixin-metadata.ts#L30.

Description of changes

Use withMixins, which calls the correct applyMixin function. Reflects the behaviour in CfnElement and Resource.

Describe any new or updated permissions being added

No new permissions are added.

Description of how you validated changes

No new permissions are added.

Checklist

• My code adheres to the CONTRIBUTING GUIDE and DESIGN GUIDELINES

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By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license

[aws-cdk-automation]

(This review is outdated)

✅ Updated pull request passes all PRLinter validations. Dismissing previous PRLinter review.

[github-actions]

⚠️ Experimental Feature: This security report is currently in experimental phase. Results may include false positives and the rules are being actively refined.
This security report is NOT a review blocker. Please try merge from main to avoid findings unrelated to the PR.

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	Tests	Passed ✅	Skipped	Failed
Security Guardian Results	48 ran	48 passed

Test	Result
No test annotations available

• View Security Guardian Results

[github-actions]

⚠️ Experimental Feature: This security report is currently in experimental phase. Results may include false positives and the rules are being actively refined.
This security report is NOT a review blocker. Please try merge from main to avoid findings unrelated to the PR.

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	Tests	Passed ✅	Skipped	Failed
Security Guardian Results with resolved templates	48 ran	48 passed

Test	Result
No test annotations available

• View Security Guardian Results with resolved templates

[mergify]

Thank you for contributing! Your pull request will be updated from main and then merged automatically (do not update manually, and be sure to allow changes to be pushed to your fork).

[mergify]

Merge Queue Status

• ✅ Entered queue — 2026-03-24 11:57 UTC · Rule: default-squash
• ✅ Checks passed · in-place
• ✅ Merged — 2026-03-24 12:43 UTC · at 92874912c5402159bdbafa0eef1af71644d84c89

This pull request spent 45 minutes 48 seconds in the queue, including 45 minutes 37 seconds running CI.

Required conditions to merge

• #approved-reviews-by >= 1 [🛡 GitHub branch protection]
  • fix(mixin): use withMixin in Stack to set mixin metadata in its constructs #37269
• #changes-requested-reviews-by = 0 [🛡 GitHub branch protection]
  • fix(mixin): use withMixin in Stack to set mixin metadata in its constructs #37269
• any of [🛡 GitHub branch protection]:
  • check-success = validate-pr
  • check-neutral = validate-pr
  • check-skipped = validate-pr
• any of [🛡 GitHub branch protection]:
  • check-success = build
  • check-neutral = build
  • check-skipped = build

[github-actions]

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