Synapse sends events over `/sync` in rooms that are mid-faster-join, to clients that don't support membership lazy-loading

### Description

Synapse appears to send new events down sync for clients that don't support lazy loading.
This leads to clients having rooms that contain no state events.

Example in nheko:

### Steps to reproduce

- Join one or more "large" rooms (~150-200 in my case)
- Notice new "empty rooms" appearing in client as people send messages, join/leave, ...

### Homeserver

rory.gay

### Synapse Version

1.114.0

### Installation Method

Other (please mention below)

### Database

PostgreSQL 16.4, single db, no portdb/restores

### Workers

Multiple workers

### Platform

NixOS, VM with 256GiB of RAM and 14 threads off an AMD Epyc 7262
(Synapse from nixpkgs/master)

### Configuration

Presence: on
Message retention: not configured
Experimental features: MSCs 2815, 3026, 3266, 3916, 3823, 4151

### Relevant log output

```shell
None, sync workers only appear to log "Processed request" (CS-API) and "Received response" (replication), no warnings emitted (INFO loglevel)
```

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

*This is a single person homeserver!* This may not be reproducible if the homeserver already has a local copy of the room.

Please probe me on Matrix ([matrix:u/emma:rory.gay](matrix:u/emma:rory.gay)) if more information is needed, as I don't actively monitor GitHub or email.