Update github summary wth action's results

Question

I would like to modify our the GHE workflow summary with some action's results using GITHUB_STEP_SUMMARY

Here is how it is organized:

1. From the web UI or gh CLI, we launch a generic workflow which build a matrix based on some module's configuration file.
2. The generic workflow calls a specific workflow (e.g: build_and_test)
3. The specific workflow calls a set of composite actions (like build, test and so on).

I would like to build a summary from some actions's results.

I first tried using parameters to "escalate" the workflow layers (action->specific workflow->generic workflow) and then with GITHUB_ENV, but it looks that this last option is owned by the file and not the entire mechanic.