The call of TAG SOURCES for samplers with different artists differs for MUSICBRAINZ and DISCOGS.
When MUSICBRAINZ is called, the misleading artist of the first track is transferred, not the ALBUMARTIST.
Is this a bug or a feature?
Could you please show us a real example to reproduce this behaviour?
I assume, you are referring to these two releases:
MB: https://musicbrainz.org/release/297286cc-20fa-44ac-9113-025068ccb3e5
DG: https://www.discogs.com/de/release/1727357-Various-The-Monterey-International-Pop-Festival
In both cases, I get Various Artists or Various in ALBUMARTIST:
MB:
DG:
Can you please describe in more details, what you would expect to see in ALBUMARTIST?
Or do you ask why the initial DG search call is builded with
[SearchBy]=Artist||$if2(%albumartist%,%artist%)...
and the initial MB search call is builded with
[SearchBy]=...Artist||$if(%artist%,$regexp(%artist%,'[+!(...
Because the search with Various Artist (= albumartist) instead of John Phillips (artist of first song on disc1) brings wrong results.
The search in discogs immediately brings up the right entries.
In Discogs the Artistname of album-compilations is "Various" instead of "Various Artists".
So you have to search for "Various".
If you have filled your albumartist-fiels with "Various Artists" and don't want to change the search manually each time you can change the script to
[SearchBy]=Artist||$if2($replace(%albumartist%,Various Artists,Various),%artist%)||&artist=%s||Album||%album%||&release_title=%s
Searches in both DISCOGS and MUSICBRAINZ generally return the correct results if you start with the correct search terms.
However, when searching in MUSICBRAINZ, MP3Tag always suggests the artist of the first track, even though ALBUMARTIST contains the correct value 'Various Artists'.
Everything can be corrected manually, but the values for the correct programme logic are available.
The Monterey album is just one example of this behaviour.
You are right for the MUSICBRAINZ-script. It searches for %artist% instead of %albumartist%. This was the same with discogs some time ago. I think a lot of people still don't fill their albumartist-tagfield.
I myself habve been using ALBUMARTIST soon after starting with tagging mp3s and for compilations I use "Various Artists" for ALBUMARTIST. So it decided to change the scripts manually to use %albumartist% for search. But it was a little annoying that after every mp3tag-update the official scripts were replaced again. Therefore I decided to rename my edited scripts. The official websource scripts don't get so often changed and so it its much lesser effort to look now and then if something has changed than editing the script after each update.
As I wrote above I changed the Discogs script "Artist+Album" this way:
[SearchBy]=Artist||$if2($replace(%albumartist%,Various Artists,Various),%artist%)||&artist=%s||Album||%album%||&release_title=%s
As Discogs internally uses "Various" instead of "Various Artists" I had to change the official script for my use. Discogs often shows results for "Various Artists" but in very much cases I get "Sorry, no entries are matching your search criteria" if I don't use the replace-function.
For Musicbrainz I changed the script to:
[SearchBy]=Album||$regexp(%album%,'[+!(){}\[\]^"~*?:\\]',)||release:%s||Artist||$if($if2(%albumartist%,%artist%),$regexp($if2(%albumartist%,%artist%),'[+!(){}\[\]^"~*?:\\]',),)||%20AND%20artist:%28%s%29
As I am far away from being good in scripting I think there may be better ways to achieve the goal but it seems to work for me. Maybe someone can improve the script.
Anyway I suggest to change all official scripts the way to prefer ALBUMARTIST if there is content in the tag.
Maybe the discogs-script should be changed to:
[SearchBy]=Artist||$if2($replace(%albumartist%,Various Artists,Various,VA,Various,Diverse,Various),%artist%)||&artist=%s||Album||%album%||&release_title=%s
I think the replace-pairs should even be more respecting language differences.
I didn't know 
that each user can or must manage their own search scripts.
Where can I find the scripts?
Can the return fields also be configured?
Menu File -> Open Configuration Folder -> Open the folder \data -> Open the folder \sources
Yes. But you need to know some scripting knowledge.
If you just want to deselect some fields, then you can enable/disable them directly in the search result window called "Adjust tag information" of your script.