🚸(backend) on user search match emails by Levenstein distance

When the query looks like an email (includes @) we search by
Levenstein distance because we are just trying to prevent typing
errors, not searching anymore.

It is important to still propose results with a short Levenstein
distance because it is frequent to forget a double letter in
someone's name for example "Pacoud" or even "pacou" instead of
"Paccoud" and we want to prevent duplicates or failing on
invitation.

We consider the query string to be an email as soon as it contains
a "@" character. Trying harder to identify a string that is really
an email would lead to weird behaviors like toto@example.gouv looking
like and email but if we continue typing toto@example.gouv.f not
looking like an email... before toto@example.gouv.fr finally looking
like an email. The result would be jumping from one type of search
to the other. As soon as there is a "@" in the query, we can be
sure that the user is not looking for a name anymore and we can
switch to matching by Levenstein distance.

src/backend/core/api/viewsets.py

@@ -20,6 +20,7 @@ from django.db.models import (
     Subquery,
     Value,
 )
+from django.db.models.expressions import RawSQL
 from django.http import Http404
 
 import rest_framework as drf
@@ -150,29 +151,35 @@ class UserViewSet(
         """
         queryset = self.queryset
 
-        if self.action == "list":
-            # Exclude all users already in the given document
-            if document_id := self.request.GET.get("document_id", ""):
-                queryset = queryset.exclude(documentaccess__document_id=document_id)
+        if self.action != "list":
+            return queryset
 
-            # Filter users by email similarity
-            if query := self.request.GET.get("q", ""):
-                # For performance reasons we filter first by similarity, which relies on an index,
-                # then only calculate precise similarity scores for sorting purposes
-                queryset = queryset.filter(email__trigram_word_similar=query)
+        # Exclude all users already in the given document
+        if document_id := self.request.GET.get("document_id", ""):
+            queryset = queryset.exclude(documentaccess__document_id=document_id)
 
-                queryset = queryset.annotate(
-                    similarity=TrigramSimilarity("email", query)
+        if not (query := self.request.GET.get("q", "")):
+            return queryset
+
+        # For emails, match emails by Levenstein distance to prevent typing errors
+        if "@" in query:
+            return (
+                queryset.annotate(
+                    distance=RawSQL("levenshtein(email::text, %s::text)", (query,))
                 )
-                # When the query only is on the name part, we should try to make many proposals
-                # But when the query looks like an email we should only propose serious matches
-                threshold = 0.6 if "@" in query else 0.1
+                .filter(distance__lte=3)
+                .order_by("distance", "email")
+            )
 
-                queryset = queryset.filter(similarity__gt=threshold).order_by(
-                    "-similarity", "email"
-                )
-
-        return queryset
+        # Use trigram similarity for non-email-like queries
+        # For performance reasons we filter first by similarity, which relies on an
+        # index, then only calculate precise similarity scores for sorting purposes
+        return (
+            queryset.filter(email__trigram_word_similar=query)
+            .annotate(similarity=TrigramSimilarity("email", query))
+            .filter(similarity__gt=0.2)
+            .order_by("-similarity", "email")
+        )
 
     @drf.decorators.action(
         detail=False,