/members endpoint incorrectly returning 403

### Description

I created a DM over federation. Upon the room being created, I sent a message in Element-Web, which refused to send due to: `Error sending event M_FORBIDDEN: MatrixError: [403] User @kegan:matrix.org not allowed to view events in room !LFuqCQZUwZtXTLWLLw:matrix.org at token StreamToken(room_key=RoomStreamToken(stream=4697475137, instance_map=immutabledict({'event_persister-5': 4697475604, 'event_persister-4': 4697475604, 'event_persister-2': 4697475604, 'event_persister-1': 4697475604}), topological=None), presence_key=757284974, typing_key=323532, receipt_key=MultiWriterStreamToken(stream=2638193413, instance_map=immutabledict({})), account_data_key=2822308049, push_rules_key=5248105, to_device_key=1268713876, device_list_key=9889126520, groups_key=0, un_partial_stated_rooms_key=239350)`. This is clearly in error, as _I created the room_.

As far as I can tell either:
- the token I got is too far behind and the worker is correctly saying that well before that point the room didn't exist (or did exist but prior to the `m.room.member` join event for myself)
- or the worker that I hit on matrix.org is too far behind and was unaware that the room existed.

Waiting a while and retrying to send a message eventually worked. DMs are E2EE hence in order to send messages the client will first hit `/members` for an up-to-date member list.

Anoa says that https://github.com/element-hq/synapse/blob/23740eaa3da94fbe2e25180376961979fc4e8cd3/synapse/rest/client/room.py#L627-L632 eventually goes through to https://github.com/element-hq/synapse/blob/23740eaa3da94fbe2e25180376961979fc4e8cd3/synapse/handlers/message.py#L212-L219 where the error is being returned.

### Steps to reproduce

Unknown. Created a DM over federation and sent a message (not particularly quickly either!).

### Homeserver

matrix.org

### Synapse Version

`1.101.0 (b=matrix-org-hotfixes,6dbedcf601)`

### Installation Method

I don't know

### Database

PostgreSQL

### Workers

Multiple workers

### Platform

-

### Configuration

_No response_

### Relevant log output

```shell
2024-02-13 14:59:06,115 - synapse.http.server - 130 - INFO - GET-854deeeb1b0a2216-MAN -
SynapseError: 403 - User @kegan:matrix.org not allowed to view events in room !LFuqCQZUwZtXTLWLLw:matrix.org at token StreamToken(room_key=RoomStreamToken(stream=4697475137,
instance_map=immutabledict({'event_persister-5': 4697475604, 'event_persister-4': 4697475604, 'event_persister-2': 4697475604, 'event_persister-1': 4697475604}), topological=None),
presence_key=757284974, typing_key=323532, receipt_key=MultiWriterStreamToken(stream=2638193413, instance_map=immutabledict({})), account_data_key=28223080
49, push_rules_key=5248105, to_device_key=1268713876, device_list_key=9889126520, groups_key=0, un_partial_stated_rooms_key=239350)
2024-02-13 14:59:06,116 - synapse.access.http.11108 - 472 - INFO - GET-854deeeb1b0a2216-MAN - redacted - 11108 - {@kegan:matrix.org} Processed request:
0.006sec/0.000sec (0.004sec, 0.000sec) (0.000sec/0.002sec/2) 657B 403 "GET /_matrix/client/v3/rooms/!LFuqCQZUwZtXTLWLLw%3Amatrix.org/members?not_membership
=leave&at=m4697475137%7E37.4697475604%7E36.4697475604%7E2.4697475604%7E1.4697475604_757284974_323532_2638193413_2822308049_5248105_1268713876_9889126520_0_2
39350 HTTP/1.1" "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Element/1.11.57 Chrome/120.0.6099.199 Electron/28.1.
3 Safari/537.36" [0 dbevts]
```

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

_No response_