When selecting Document Status = open, the resulting SQL query has an additional condition user_user_fdocument.isClosed = 0.
That is false for e.g. Anna in the DB having isClosed = 1, while other users which are correctly found have isClosed = 0:

mysql:phstats@m3-slave.eqiad.wmnet [phabricator_user]> SELECT u.userName, f.* FROM user_user_fdocument f INNER JOIN user u ON u.phid = f.objectPHID WHERE f.objectPHID = "PHID-USER-gjeg26or67pbqd6rk2aw" OR f.objectPHID = "PHID-USER-j2ysgbht5lbabsrdyvwm";
+------------------+-------+--------------------------------+----------+------------+-----------+--------------+---------------+
| userName         | id    | objectPHID                     | isClosed | authorPHID | ownerPHID | epochCreated | epochModified |
+------------------+-------+--------------------------------+----------+------------+-----------+--------------+---------------+
| Eric_Luth_WMSE   | 17393 | PHID-USER-gjeg26or67pbqd6rk2aw |        0 | NULL       | NULL      |   1472458662 |    1540903683 |
| Anna_Jegeus_WMSE | 41452 | PHID-USER-j2ysgbht5lbabsrdyvwm |        1 | NULL       | NULL      |   1707296891 |    1707296891 |
+------------------+-------+--------------------------------+----------+------------+-----------+--------------+---------------+

ft_doc.isClosed is read as a parameter in PhabricatorCursorPagedPolicyAwareQuery.

It seems isClosed is written in https://phabricator.wikimedia.org/source/phabricator/browse/wmf%252Fstable/src/applications/search/engineextension/PhabricatorFerretFulltextEngineExtension.php$26-48 which sets PhabricatorSearchRelationship::RELATIONSHIP_CLOSED for some reason.

That reason comes from $type in PhabricatorSearchAbstractDocument::addRelationship($type, $related_phid, $rtype, $time).

I assume that's called in PhabricatorUserFulltextEngine::buildAbstractDocument which checks for

$user->isUserActivated()
  ? PhabricatorSearchRelationship::RELATIONSHIP_OPEN
  : PhabricatorSearchRelationship::RELATIONSHIP_CLOSED,

PhabricatorUser:isUserActivated() checks if an account is "enabled, verified (if required), approved (if required)" and returns false if not.
We require validation (means: email) per https://phabricator.wikimedia.org/config/edit/auth.require-email-verification/ : "email addresses must be verified (by clicking a link in an email) before a user can login".

So I wonder if this account got indexed (not sure how that is triggered) before it got "verified".
And whether there is any code to ever reindex when verification happened in the meantime.

That entry in ftdoc was created at 1707296891. It does not look like Phab logs when an account got verified though.

I ran
SELECT u.userName fdoc FROM phabricator_user.user_user_fdocument f INNER JOIN phabricator_user.user u ON u.phid = f.objectPHID WHERE f.isClosed = 1 AND u.isDisabled = 0 AND u.isEmailVerified = 1 AND u.isApproved = 1 AND u.isMailingList = 0;
and then I reindexed the resulting users via
sudo ./bin/search index --force --background @Alice @Bob @Charlie @etc

Obviously won't fix the next user to register an account (see my previous comment) but global search results for open users should be rather complete for now at least.

Note to myself: I finally got to the root problem and proposed https://we.phorge.it/D26553 in upstream.
Once pulled and deployed in our instance, still need to fix the existing DB entries manually.