AFAICT, VisualEditor already performs the perfect API call that will receive mediasearch results once the new profile is activated by default (so: blocked on T262271)
Work for this ticket will likely be a simple verification.

@matthiasmullie does that mean that when we complete T262271 that Visual Editor will automatically switch to using MediaSearch? What about default Commons search?

Yes for VE.

Default Commons search: yes, under certain conditions (=only searching NS_FILE namespace), which are not the default conditions (other namespaces are also selected by default).
So barely any "default search" sessions will likely use mediasearch profile.

That's very good to know, thanks! I'm going to add the ReleaseCandidate milestone to T262271 and put a note that we should make sure we're confident before we go ahead and merge that one.

@matthiasmullie will this affect file namespace searches on the wikipedias?

In T259896#6474685, @CBogen wrote:

@matthiasmullie will this affect file namespace searches on the wikipedias?

No. While it uses the same search index, it doesn't use the Commons-specific media search profile. Wikipedia's file search results will not change.

Change 631394 had a related patch set uploaded (by Matthias Mullie; owner: Matthias Mullie):
[mediawiki/core@master] Search files in user language

https://gerrit.wikimedia.org/r/631394

Change 631394 merged by jenkins-bot:
[mediawiki/core@master] Search files in user language

https://gerrit.wikimedia.org/r/631394

@ppelberg just a heads up that this has been merged and will be on next week's train!

@matthiasmullie the description of this task talks about passing through the interface language - is that part of this patch or should we remove it from the description/file it as a future enhancement?

Yes, that is in the patch that has been merged.

Adding User-notice as this is included in the upcoming publication of Tech News.