[proposal] Deploy a matrix-connection-tester-ui on a subdomain of matrix.org

I'd like to discuss whether it might be possible to deploy a [matrix-connection-tester-ui](https://github.com/MTRNord/matrix-connection-tester-ui/) on a subdomain of matrix.org.

Currently, there is federationtester.matrix.org which uses [fed-tester-ui](https://github.com/matrix-org/fed-tester-ui) and [matrix-federation-tester](https://github.com/matrix-org/matrix-federation-tester).

The currently deployed federation tester is flaky and much less advanced than the work of @MTRNord . In order to have an intuitively accessible and coherent way for homeserver admins to ensure their deployments meet the requirements for public federation, The Matrix.org Foundation as the operator of the Matrix.org website should provide up-to-date resources for admins to check their deployment.

I'd propose to keep federationtester.matrix.org deployed as is for compatibility reasons and deploy a matrix-connection-tester-ui in addition, maybe with a note recommending the new site for the legacy site.

I'd like to have this discussed by the Website WG, the community and the admins whether this could be a future-leading approach on reliable public federation monitoring.

Start by reviewing the current federationtester.matrix.org deployment and the linked fed-tester-ui, matrix-federation-tester, and matrix-connection-tester-ui projects. The issue calls for discussion by the Website WG, community, and admins; done would require an agreed approach and a defined plan for deploying the new UI while preserving the legacy site.

Written by the indexing model from the issue text.