Add check to a specific workflow-run/check-suite using octokit - github-actions

Question

I have a project with Github Actions that implements multiple workflows that can be triggered by a single push event (depending on path filter).
So a push with a single commit can trigger multiple workflows, so far so good.
In each workflow I am running actions/github-script to create dynamic run-checks with the following step:
- uses: actions/github-script#v4
with:
github-token: ${{ inputs.github-token }}
script: |
const date = new Date();
const check = await github.checks.create({
owner: "${{ steps.vars.outputs.owner }}",
repo: "${{ steps.vars.outputs.repo }}",
name: "Custom Script",
started_at: date.toISOString(),
completed_at: date.toISOString(),
head_sha: "${{ inputs.sha }}",
external_id: "${{ github.run_id }}",
status: "completed",
conclusion: "success",
output: {
title: "Some funny title",
summary: "Build successful",
text: "Image pushed to https://${{ inputs.region }}.console.aws.amazon.com/ecr/repositories/private/${{ inputs.customer-id }}/modix/base/${{ inputs.image }}"
}
});
It is working like a charm, when a single workflow is triggered, but as soon as a push triggers multiple workflows, then only the first one that runs is showing the added check. all others but the first don't show the check but also no error?
Before I have tried the LouisBrunner/checks-action and it had the same problem so I created an issue: https://github.com/LouisBrunner/checks-action/issues/26. But now that it also fails by directly using octokit with github-script action, it feels like the problem is somewhere else...
UPDATE:
According to Gregors answer, I have tried giving the check a different name in each workflow by appending the run-id, I found that each parallel workflow is adding the check to the workflow that runs first... so the question now is, how to send it to a specific workflow run?
according to these docs, there is no dedicated parameter for that, it seems that it automatically detects the workflow using the head_sha?
name: "Custom Script ${{ github.run_id }}",

Answer 1

Try setting Custom Script to something different for each check run you create. I think multiple check runs with the same names are collapsed into only showing the last one. The reason is that that way you can override an status on a commit, by using the same name.

Answer 2

Sadly I found that it is simply impossible to attach a check to a specific workflow-run or check-suite. The problem is known for over a year now, but they didn't provide any solution yet. See in this thread.
In the name of a big automotive company, I have now submitted a feature request in the official feedback form of github.
PS: If the feature will be implemented in the future, I am going to create and accept another answer here.