@IvanDobsky Ivan
The URL you have shown is a normal web search. Picard uses the Indexed Search instead and as per Metatag not properly recognised this does not use the alias table when searching.
I suspect that this is the search that Picard will use:
https://musicbrainz.org/search?query=artist%3A%28Ad%C3%A8le%29+&type=artist&limit=25&method=advanced
and this does return Adele.