Licence information comes from two places:

When fetching Articles/Pages/Talk/etc on Wikis - it comes from configuration -

	'url' => $this->options->get( MainConfigNames::RightsUrl ),
	'title' => $this->options->get( MainConfigNames::RightsText )

source: https://gerrit.wikimedia.org/r/plugins/gitiles/mediawiki/core/+/2efa5409d70bb2437cbd2c3276f1f96264961f2a/includes/Rest/Handler/Helper/PageContentHelper.php#258

This one is relatively easy to do - we would need to go through configs. ( https://gerrit.wikimedia.org/g/operations/mediawiki-config/+/3ff486473879abe7eafcf61e60f09784ee5071eb/wmf-config/InitialiseSettings.php#11368 ) and most likely provide a new config RightsTextShort .

When fetching media it comes from templates

This licence info comes from templates - texts are stored on all projects as freehand text.

For example - the template for CC-BY-SA-4.0 on Commons renders ( source: https://commons.wikimedia.org/wiki/Template:Cc-by-sa-4.0 )

<div class="rlicense-text">
  <span class="licensetpl_link" style="display:none;">https://creativecommons.org/licenses/by-sa/4.0</span>
  <span class="licensetpl_short" style="display:none;">CC BY-SA 4.0 </span>
  <span class="licensetpl_long" style="display:none;">Creative Commons Attribution-Share Alike 4.0 </span>
  <span class="licensetpl_link_req" style="display:none;">true</span>
  <span class="licensetpl_attr_req" style="display:none;">true</span>
</div>

Then the CommonsMetadata extracts from rendered template elements with .licensetpl_short, .licensetpl_link, .licensetpl_long etc.
Then, this template may be different, for example on Polish Wikipedia ( source: https://pl.wikipedia.org/wiki/Szablon:CC_BY-SA_4.0 )

<span class="licensetpl" style="display:none;">
  <span class="licensetpl_link">https://creativecommons.org/licenses/by-sa/4.0</span>
  <span class="licensetpl_short">CC BY-SA 4.0</span>
  <span class="licensetpl_long">Creative Commons Attribution-Share Alike 4.0</span>
  <span class="licensetpl_link_req">true</span><span class="licensetpl_attr_req">true</span>
</span>

It's almost the same, but you can see that they're two different templates; people can enter whatever they want. We can try to fix some stuff in flight, but we won't be able to make it 100% correct for every case/scenario.
I wouldn't use any regex magic here; this info comes from templates, and those aren't edited often. IMHO it's better to create a map and map some of those into other:

$standarizedLicenceShortTextMap = [
  'PD' => 'PDM',
  'PUBLIC DOMAIN' => 'PDM',
  ...
];

$licenceShort = mb_strtoupper( $licenceShort );
return $standarizedLicenceShortTextMap[$licenceShort] ?? $licenceShort;

The regex magic may return some weird output on our texts, the one attached for sure will fail when whitespaces are mixed ( added extra or removed )

I submitted T421051: Attribution - Align Media licence information with Article licence information to standardize licence information between Articles and Media as for now - one returns a long text licence text, and second returns short text.

In T420784#11742463, @pmiazga wrote:

I wouldn't use any regex magic here; this info comes from templates, and those aren't edited often. IMHO it's better to create a map and map some of those into other:

$standarizedLicenceShortTextMap = [
  'PD' => 'PDM',
  'PUBLIC DOMAIN' => 'PDM',
  ...
];

$licenceShort = mb_strtoupper( $licenceShort );
return $standarizedLicenceShortTextMap[$licenceShort] ?? $licenceShort;

The regex magic may return some weird output on our texts, the one attached for sure will fail when whitespaces are mixed ( added extra or removed )

Yeah I agree, licenses are fairly standardized in the templates, but what you could do is do a "soft" combination of both regex and a map, where you use regex only for spaces-or-dashes and capitalization normalization.

Something like

$standarizedLicenceShortTextMap = [
  'PD' => 'PDM',
  'PUBLIC[ -]?DOMAIN' => 'PDM',
  'CC[ -]+?by[ -]+?SA[ -]+?3.0' => 'CC-by-SA 3.0'
  ...
];

And then run this through a regex with /i to be case insensitive. This can then normalize in our own map uses of CC-by-SA 3.0 vs CC by SA-3.0 vs CC by SA - 3.0 that may differ a little in weird places but all mean the same.