Local users don't always appear first even with `prefer_local_users: true`

This issue has been migrated from [#15521](https://github.com/matrix-org/synapse/issues/15521).

---

### Description

This might be somewhere between bug and feature request, since the description of the configuration setting says it *prefers* them but does not put them first. Depending on the use case (i.e. schools and other organizations), it is ideal to show the local users first and foremost.

> prefer_local_users: Defines whether to prefer local users in search query results. If set to true, local users are **more likely** to appear above remote users when searching the user directory. Defaults to false.

### Steps to reproduce

1. In `homeserver.yaml` config, set `prefer_local_users: true`
1. Search for a user by localpart using `/user_directory/search`
1. Notice that results from my homeserver (`matrix.mit.edu`) appears in fourth place whereas I expected it to be above the other remove homeservers.



### Homeserver

matrix.mit.edu

### Synapse Version

1.81.0+jammy1

### Installation Method

Debian packages from packages.matrix.org

### Database

Single PostgreSQL 14+238 server, no ports or restores

### Workers

Single process

### Platform

Ubuntu 20.04

### Configuration

```
user_directory:
enabled: true
search_all_users: true
prefer_local_users: true
```

### Relevant log output

```shell
{@rgabriel:matrix.mit.edu} Processed request: 0.027sec/0.000sec (0.000sec, 0.000sec) (0.000sec/0.017sec/1) 554B 200 "POST /_matrix/client/r0/user_directory/search HTTP/1.1" "Mozilla/5.0 (X11; Linux x86_64; rv:109.0) Gecko/20100101 Firefox/112.0" [0 dbevts]
```

### Anything else that would be useful to know?

_No response_

Related: #12958 (asks for ability to only show local users, this is an in-between)

Start by tracing the /user_directory/search endpoint and the prefer_local_users setting described in homeserver.yaml, then inspect how search results are ordered. Compare the current behavior with the documented preference and the reproduction; done means local users consistently appear before remote users when the setting is enabled.

Written by the indexing model from the issue text.