Add manifest-building GHA

[tcompa]

Checklist before merging

• I added an appropriate entry to CHANGELOG.md

[github-actions]

Coverage report

This PR does not seem to contain any modification to coverable code.

[tcompa]

I'm merging this PR, with the following option for the new GitHub Action:

on:
  push:
    branches: ["main"]
  pull_request:
    branches: ["main"]
  workflow_dispatch:
  schedule:
    - cron: "0 23 * * 3"

which makes it run at every PR towards main, at every push to main and every Wednesday.

If it turns out that this creates too much friction for standard PRs, we can move back to only running on given days of the week and not on PRs.