The non-square logo doesn't preserve the aspect ratio.
Suspect: the <img> for logo has the object-fit set as fill.
Example:
https://florencia.wikibase.cloud/wiki/Main_Page
https://mywayordatwayy.wikibase.cloud/wiki/Main_Page
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Currently the application is designed to specifically support square logos; this is reflected in the help text for the logo selector.
The actual logo that is visible on the wiki is one that is scaled to the recommended Mediawiki logo specification (https://www.mediawiki.org/wiki/Manual:$wgLogos). According to this it should be nominally square but there is some play for stretching in the height direction.
This scaling is an active process we undertake so that it looks "sensible" in case people upload them at the wrong size; I guess nobody took into account that the logo that is uploaded could be non-square. You can look at the backend job we have for logo resizing here (as well as favicon creation here) https://github.com/wbstack/api/blob/a42a12d9c947579654196ee2205537e133df1be9/app/Jobs/SetWikiLogo.php#L33
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From technical refinement: @Evelien_WMDE please specify the desired outcome of how the logo is supposed to look. Additionally, how should the user story of users uploading non-square logos work?
Additionally caveat: With further upgrades of MediaWiki, we will include further optional skins that have an impact on how logos are being displayed.