Server Admin can't re-join room

### Description

If server admin accidentally leve (probably also kicked) from the space, there is no way how to get back to space (only direct DB manipulation).

This is very frustrating.
There is use case, that some external system wants synchronize users / spaces to correspond this system universe. But if this happen, synchronisation breaks because if this admin is not in space, can't manage users in it, and even ADMIN can't get back (not federated use-case but local ones).

I tried everything - probably BUG or is not possible at all (which is, IMO, stupid).

### Steps to reproduce

AS admin:

- create space
- leave space
- try to get back

### Homeserver

local one

### Synapse Version

1.139.1

### Installation Method

Docker (matrixdotorg/synapse)

### Database

sqlite and postgres

### Workers

Single process

### Platform

Dockerized on Debian GNU/Linux 12 (bookworm)

### Configuration

_No response_

### Relevant log output

```shell
matrix_synapse | 2025-11-14 08:39:28,492 - synapse.http.server - 135 - INFO - POST-9680 - SynapseError: 403 - @admin:server not in room !vXv1Q...CENSORED.
```

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

_No response_