`last_seen_ts` in `/client/r0/devices` is out of date

This issue has been migrated from [#16084](https://github.com/matrix-org/synapse/issues/16084).

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### Description

When querying the devices list it seems like `last_seen_ts` is out of date.

### Steps to reproduce

- Have some devices
- Query them via `/_matrix/client/r0/devices`

I know I have devices, that I recently used.
All returned `last_seen_ts` are out of date.

### Homeserver

element.ems.host

### Synapse Version

1.89.0

### Installation Method

I don't know

### Database

-

### Workers

I don't know

### Platform

-

### Configuration

_No response_

### Relevant log output

```shell
-
```

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

_No response_