Showing Mutual Rooms

This is a request to implement [MSC2666](https://github.com/matrix-org/matrix-spec-proposals/pull/2666) across Element.

Previously, https://github.com/matrix-org/matrix-react-sdk/pull/4897 had been in the works to add this to element-web, but it did not reach completion before I picked up MSC2666. Afterwards I found it hard to resume that PR.

This feature has already been added to js-sdk (https://github.com/matrix-org/matrix-js-sdk/pull/1417 and subsequent iterations).

This issue is a request to implement it in respective SDKs across Element, and to come up with a common design for this, likely stemming from the work in https://github.com/matrix-org/matrix-react-sdk/pull/4897.

Start by reading MSC2666, the existing matrix-js-sdk implementation in PR 1417 and later iterations, and the incomplete matrix-react-sdk PR 4897. Determine how the feature should be implemented across the respective Element SDKs and establish a common design; done means the SDK implementations and shared design are complete.

Written by the indexing model from the issue text.