The following experimental modification (removing "index.php?title=" from the resource attribute) seems to fix the issue for my installation:

diff --git a/extensions/VisualEditor/modules/ve-mw/dm/annotations/ve.dm.MWInternalLinkAnnotation.js b/extensions/VisualEditor/modules/ve-mw/dm/annotations/ve.dm.MWInternalLinkAnnotation.js
index fdf9a01b..ce1acf10 100644
--- a/extensions/VisualEditor/modules/ve-mw/dm/annotations/ve.dm.MWInternalLinkAnnotation.js
+++ b/extensions/VisualEditor/modules/ve-mw/dm/annotations/ve.dm.MWInternalLinkAnnotation.js
@@ -38,8 +38,8 @@ ve.dm.MWInternalLinkAnnotation.static.allowedRdfaTypes = [ 'mw:Error' ];
 ve.dm.MWInternalLinkAnnotation.static.toDataElement = function ( domElements, converter ) {
        var targetData,
                resource = domElements[ 0 ].getAttribute( 'resource' );
-
        if ( resource ) {
+               resource = resource.replace("index.php%3Ftitle=","");
                targetData = mw.libs.ve.parseParsoidResourceName( resource );
        } else {
                targetData = mw.libs.ve.getTargetDataFromHref(

Also, although normal links do not get corrupted in the same way, editing them still tags the "index.php?title=" in the input box as an invalid link (see screenshot below)

Parsoid and VisualEditor basically assume that you have short URLs set up on your wiki (or at least that you have $wgUsePathInfo enabled). I've recently ran into similar problems (https://gerrit.wikimedia.org/r/c/mediawiki/services/parsoid/+/623873 / T261711). This would probably take lots of work to fix and I don't really see it happening… Sorry.

In T265144#6534835, @matmarex wrote:

Parsoid and VisualEditor basically assume that you have short URLs set up on your wiki (or at least that you have $wgUsePathInfo enabled). I've recently ran into similar problems (https://gerrit.wikimedia.org/r/c/mediawiki/services/parsoid/+/623873 / T261711). This would probably take lots of work to fix and I don't really see it happening… Sorry.

It used to be working in 1.33...I am not even talking about media link, just normal links.