Forgetting a room doesn't clear sync cache

This issue has been migrated from [#15147](https://github.com/matrix-org/synapse/issues/15147).

---

### Description

I left a room, `/forget` it, and it was still appearing under "historical" after refreshing my client. In another client, the room was still appearing in the initial sync.

### Steps to reproduce

1. Create a room
2. Initial sync a device
3. Leave the room
4. Forget the room
5. Re-initial sync the device from step 2

### Homeserver

localhost

### Synapse Version

1.77.0

### Installation Method

Docker (matrixdotorg/synapse)

### Database

postgres 13

### Workers

Single process

### Platform

docker

### Configuration

_No response_

### Relevant log output

```shell
element-dev-stack-eledev-synapse-1 | 2023-02-23 22:07:54,122 - synapse.util.caches.response_cache - 260 - INFO - GET-212 - [sync]: using completed cached result for [(@demo:localhost, 10000, None, '2', False, 'WMHLYEWEDG')]
element-dev-stack-eledev-synapse-1 | 2023-02-23 22:07:54,123 - synapse.access.http.8008 - 460 - INFO - GET-212 - 172.26.0.5 - 8008 - {@demo:localhost} Processed request: 0.001sec/0.000sec (0.001sec, 0.000sec) (0.000sec/0.000sec/0) 3129B 200 "GET /_matrix/client/v3/sync?filter=2&timeout=10000& HTTP/1.0" "okhttp/4.10.0" [0 dbevts]
```

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

restarting synapse works