`/room_summary` has the wrong default for `join_rule` being omitted

*Spawning from https://github.com/element-hq/synapse/pull/20205#discussion_r4008685789*

**Suggestion**

The current [`/room_summary` spec](https://spec.matrix.org/v1.18/client-server-api/#get_matrixclientv1room_summaryroomidoralias) says that the room is assumed to be `public` when `join_rule` isn't present but this directly contradicts the scenarios where `join_rule` doesn't exist. For example, if there is no `m.room.join_rules` event in the room, there is no default and the the [auth rules](https://spec.matrix.org/v1.18/rooms/v12/#authorization-rules) effectively make it so no one can join except the room creator. The other scenario is if `join_rule` isn't a string (not a valid `m.room.join_rules` event).

Relevant part of the spec:

> `join_rule` string
The room’s join rule. **When not present, the room is assumed to be `public`.**
>
> *-- https://spec.matrix.org/v1.18/client-server-api/#get_matrixclientv1room_summaryroomidoralias*

Start with the `/room_summary` section of the Matrix client-server API specification and compare its `join_rule` wording with the linked authorization-rules section. Update the documented behavior for missing or invalid join rules so the two sections are consistent, then check the surrounding specification text for related assumptions.

Written by the indexing model from the issue text.