Currently, HTML of the events:
-- onContentAfterTitle with an IF !show-intro condition
-- onContentBeforeDisplay
are displayed on the same place, one after the other

So both changes 'onContentAfterTitle' seem right
-- remove the IF !show-intro (and show HTML of onContentAfterTitle events always)
-- move it directly after title inside page-header box

But

1.. About IF !show-intro
-- It is a B/C break ? ... things will start appearing in some sites that were not shown before

2.. About moving HTML of onContentAfterTitle events inside "page header" ?

Yes, if someone uses onContentAfterTitle, instead of onContentBeforeDisplay,
... then the user really means to place it inside the page-header

-- but it is a (smaller) B/C break too, the page header is supposed to contain title and little / less / small stuff like the date
-- and until now it did not contain HTML of "onContentAfterTitle"

I say both changes are correct,
but it should have been like this from the beggining, now they may have unwanted side-effects to existing sites ...

It is a B/C break ? ... things will start appearing in some sites that were not shown before

Layouts aren't covered by the B/C promise. See https://developer.joomla.org/cms/development-strategy.html#backward_compatibility

6.1.7 Rendered markup
For the time being, rendered markup is not subject to our backwards compatibility promise. We will try not to change markup in such a way that a site might render differently, but we can't promise not to break anything at the present time.

things will start appearing in some sites that were not shown before

To my knowledge there is no core code that is run in the onContentAfterTitle event. That's probably why nobody noticed this bug yet. So if somethign shows up nw it is coming froma 3rd party plugin and most likely didn't behave as expected before.

I have tested this item ✅ successfully on 871c67f

One question I have, should it be inside or outside the div?
Like that

or that

Outside. IMO if it's not a part of the title it shouldn't be in the page-header div.

Moved the output outside of the page header

I have tested this item ✅ successfully on 1543eea

I have tested this item ✅ successfully on 1543eea

RTC