[core] default error handler: print info to stdout instead of stderr

[ferdymercury]

This Pull request:

Changes or fixes:

Inspired by #19479

Checklist:

• tested changes locally
• updated the docs (if necessary)

[silverweed]

Let's first discuss whether we want to do this or not in the issue.

[github-actions]

Test Results

    21 files      21 suites   3d 9h 30m 15s ⏱️
 3 222 tests  3 173 ✅ 0 💤 49 ❌
65 943 runs  65 884 ✅ 0 💤 59 ❌

For more details on these failures, see this check.

Results for commit 9f5645d.

♻️ This comment has been updated with latest results.