Better landing UI when following a matrix.to user link (update right panel)

### Your use case

#### What would you like to do?

Improve the landing experience of a user when they follow a "room invite link" like https://matrix.to/#/@alice:matrix.org

#### Why would you like to do it?

We currently use this type of links as "invites" but the landing experience is not optimised for invites at all

#### How would you like to achieve it?

Currently the only thing this will do is to open the right sidebar and show the "User Info". From there one needs to know that they should click the very tiny "Message" link to open a DM.

We should have a proper UI that is a bit more inviting

### Have you considered any alternatives?

_No response_

### Additional context

_No response_