TextExtracts removes noprint elements.

The elements of interest have

<span class="noprint navigation-not-searchable" style="white-space:nowrap;">

  <!-- {{AudioSymbol|verweis=<includeonly>{{{1}}}</includeonly>}}, this noprint seems reasonable -->
  <span class="noprint noviewer">
    <a href="/wiki/Datei:He-Ariel_Sharon.ogg" title="Audio-Datei/Hörbeispiel">
      <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/12px-Loudspeaker.svg.png" decoding="async" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/18px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/24px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" width="12" height="12">
    </a>
  </span>

  <!-- <span style="white-space:initial;">[[Media:{{{1}}}|{{{2|anhören}}}]]</span> -->
  <span style="white-space:initial;">
    <a href="//upload.wikimedia.org/wikipedia/commons/d/d0/He-Ariel_Sharon.ogg" class="internal" title="He-Ariel Sharon.ogg">
      <b>Ariel Scharon</b>
    </a>
  </span>

  <!-- <sup>[[Hilfe:Audio|<span title="Hilfe – Audio">?</span>]]/[[:Datei:{{{1}}}|<span title="Tondateibeschreibungsseite mit Lizenzangabe für „{{{1}}}“" style="font-family:monospace;">i</span>]]</sup> -->
  <sup>
    <a href="/wiki/Hilfe:Audio" title="Hilfe:Audio">
      <span title="Hilfe – Audio">?</span>
    </a>
    /
    <a href="/wiki/Datei:He-Ariel_Sharon.ogg" title="Datei:He-Ariel Sharon.ogg">
      <span title="Tondateibeschreibungsseite mit Lizenzangabe für „He-Ariel Sharon.ogg“" style="font-family:monospace;">i</span>
    </a>
  </sup>
</span>

You will want to move both noprint and navigation-not-searchable to appropriate subelements of the top-level span. The former because of this task, the latter because right now search can't see {{{2}}}, which is probably not doing wonders for [[Special:Search]] if this template is expected to be supported in this kind of location on the page.

Page previews does not use TextExtracts in WMF production code. It uses the page content service.

This may be helpful: https://m.mediawiki.org/wiki/Page_Previews/API_Specification

In T341426#9001829, @Jdlrobson wrote:

Page previews does not use TextExtracts in WMF production code. It uses the page content service.

Same issue, line 51 of summarize.js. Same way to fix.

I confirm @Izno's analysis - note we prefer standardizing content wherever possible to code changes that add to the complexity of the service. This should be reported to the relevant template and fixed on wiki.

This should be reported to the relevant template and fixed on wiki.

Where can I find instructions what exactly needs to be done on-wiki? (I guess I mostly consider this a documentation issue - I tried to find out and failed.) Thanks!

https://www.mediawiki.org/wiki/Extension:Popups#FAQ is probably the best place, but perhaps https://www.mediawiki.org/wiki/Recommendations_for_mobile_friendly_articles_on_Wikimedia_wikis should be expanded and moved to https://www.mediawiki.org/wiki/Recommendations_for_articles_on_Wikimedia_wikis to include these kind of guidelines.

@PerfektesChaos since you recently edited the template, you might take a look here and see if anything from your edit needs adjustment?

I think phab is the wrong forum for this issue. Local dewiki platforms (template discussion or general template maintenance project) are more appropriate.

My edit from 8th July did narrow noprint class to such elements which are pointless in print, while before the entire element vanished.

This was no problem in the old implementation as of 2009, as long as no content has been displayed, but just listen (this is suppressed now as well). When non-trivial information is provided, that needs to be shown. Since authors do not check a noprint preview after every edit nobody became aware.