[CDK Pipeline] Best way to share parameters cross-stage (same account)?

Another potential way is using variables in CodePipeline. We need to export variables in CodeBuild BuildSpec, then access the variables in later stages. For example, create a CodeBuild project with exported-variables

const codeBuildProject = new codebuild.PipelineProject({
    buildSpec: aws_codebuild.BuildSpec.fromObject({
         ...
         env: {
          // save the imageTag environment variable as a CodePipeline Variable
          'exported-variables': [
            'imageTag',
          ],
     }
   })
})

CodeBuild action

const codeBuildAction = new codepipeline_actions.CodeBuildAction({
      actionName: 'CodeBuildActionName',
      project: codeBuildProject,
      input: sourceOutput,
    });

then access this variable in Deploy stage

codeBuidlAction.variable('imageTag')

I hope this reference can help you