User not found is handled like session logged out

### Description

I reported [this issue](https://github.com/element-hq/element-web/issues/29517) and was told that it's caused by synapse sending the same response if a user does not exist or if a session has been logged out.

This can cause total loss of session data in some situations.

### Steps to reproduce

1. Upgrade your synapse server database server
2. Fail to correctly import your data
3. Restart synapse
4. Open element

What did you expect?

To see that the connection to the server is not working

What happened instead?

The app crashed on iOS, and went to the login screen on desktop. My session was destroyed. If I didn't have extra devices, I would have completely lost the session.

### Homeserver

self hosted

### Synapse Version

1.125.0

### Installation Method

Docker (matrixdotorg/synapse)

### Database

postgres

### Workers

Single process

### Platform

docker

### Configuration

_No response_

### Relevant log output

```shell
n/a
```

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

_No response_