Login flow for homeservers other than Matrix.org is tedious

### Your use case

Logging in to my work account (element.io) on Android Element X takes:

- three touches
- enter the server name (NOT the mxid)
- touch to select the search result
- touch to confirm
- we then start the SSO flow.

This is confusing for people who are starting with a username (mxid), because they are required to touch multiple times just to get to the point where they enter their own details, and then they need to extract the homeserver name from their username.

Ideally people could just type in their username (mxid), and the flow would begin.

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

### Are you willing to provide a PR?

No

Start by reproducing the Android Element X login flow with a full Matrix ID such as a work account on element.io, then trace the homeserver selection and SSO entry points. The change is done when a user can enter an MXID and proceed directly into the appropriate login flow without manually extracting and confirming the homeserver name.

Written by the indexing model from the issue text.