It doesn't sound like an exceptionally complicated thing to fix, but I don't even know where are these strings.

Is it in Wikibase? Or in one of the extensions or libraries on which it depends? Or is it part of wikidata.org's content?

So indeed uselang can be used to alter the error message within the parsing result.

See:

• https://test.wikidata.org/w/api.php?action=wbparsevalue&format=json&parser=globecoordinate&values=%1F36&options=%7B%22lang%22%3A%22en-gb%22%7D&uselang=en
• https://test.wikidata.org/w/api.php?action=wbparsevalue&format=json&parser=globecoordinate&values=%1F36&options=%7B%22lang%22%3A%22en-gb%22%7D&uselang=de

However the main error for the API still remains in english.

However looking at qqx the value being use there is the i18n code...
https://test.wikidata.org/w/api.php?action=wbparsevalue&format=json&parser=globecoordinate&values=%1F36&options=%7B%22lang%22%3A%22de%22%7D&uselang=qqx
But it is not being localized.

Chasing this down the pipes a bit further, this is done in ApiErrorFormetter::addMessagesFromStatus in core, which even when using uselang=de uses an EN language object for the following code:

			$msg = ApiMessage::create( $error )
				->inLanguage( $this->lang )
				->title( $this->getDummyTitle() )
				->useDatabase( $this->useDB );

Resulting in the english api output.

When testing locally it looks like ApiMain currently makes us use a ApiErrorFormatter_BackCompat instance for the call we are making.
We get this rather than a ApiErrorFormatter instance because we do not specify an error format (so the fallback bc is used)

If we specify an error format, such as "plaintext", which is consistent with the bc format, then we see the error message in the correct language.

https://test.wikidata.org/w/api.php?action=wbparsevalue&format=json&parser=globecoordinate&values=%1F36&options=%7B%22lang%22%3A%22de%22%7D&uselang=de&errorformat=plaintext

So we probably want to stop using the old bc compat layer in our UI calls to the backend, and instead specify an error format and possibly also an errorlang or uselang.

Current code snippet making the decision in ApiMain:

		$errorFormat = $request->getRawVal( 'errorformat', 'bc' );
		$errorLangCode = $request->getRawVal( 'errorlang', 'uselang' );
		$errorsUseDB = $request->getCheck( 'errorsuselocal' );
		if ( in_array( $errorFormat, [ 'plaintext', 'wikitext', 'html', 'raw', 'none' ], true ) ) {
			if ( $errorLangCode === 'uselang' ) {
				$errorLang = $this->getLanguage();
			} elseif ( $errorLangCode === 'content' ) {
				$errorLang = MediaWikiServices::getInstance()->getContentLanguage();
			} else {
				$errorLangCode = RequestContext::sanitizeLangCode( $errorLangCode );
				$errorLang = MediaWikiServices::getInstance()->getLanguageFactory()
					->getLanguage( $errorLangCode );
			}
			$this->mErrorFormatter = new ApiErrorFormatter(
				$this->mResult, $errorLang, $errorFormat, $errorsUseDB
			);
		} else {
			$this->mErrorFormatter = new ApiErrorFormatter_BackCompat( $this->mResult );
		}

Waiting on the sub ticket to be picked up and solved.

"Malformed value" was done in T242769
Precisions are not yet done (could likely do with a sub ticket

Filed T269102 for the remaining piece.