Registration doesn't keep track of the room I tried to join

### Your use case

#### What would you like to do?

It looks like we have a flaw in the onboarding flow starting with a matrix.to invite link. Steps are:

* You don't know what Matrix is, but someone invites you in a public room/you click on a [matrix.to](http://matrix.to/) link you found somewhere
* You decide to use the browser thingy because you don't know what Matrix or Element is so you don't want to install it
It tells you to either Sign Up or Sign In. You get mad at English because you never remember which one means "create an account" and which one means "login"
* After looking it up, you Sign Up on [matrix.org](http://matrix.org/)
* You provide all your information
* It tells you to confirm your email
* You click the link: it opens a new tab of Element, and you end up on an empty Element
* You can't find the conversation you were trying to join in the first place

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

I don't want registration to get in the way of joining a conversation that looked interesting.

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

The email verification seems to get in the way. Someone suggested to send a 6 digits code to confirm, which would be much less disruptive and allow to keep track of the room you tried to join in the first place.

### Have you considered any alternatives?

_No response_

### Additional context

_No response_

The issue names no files, tests, or entry points. Start by tracing the matrix.to-to-registration and email-verification flow in element-web, then determine how the originating room context is retained after verification. Done means a verified signup returns the user to the conversation they originally tried to join; the proposed six-digit code is only a suggested alternative.

Written by the indexing model from the issue text.