Pre-DM screen does not persist message on room change

[germain-gg]

Your use case

What would you like to do?

For the Pre-DM screen to persist my message

Why would you like to do it?

I've many time started writing a message to in a new DM, realised that i needed to switch rooms to copy a link, tried to go back, and lost my original message

How would you like to achieve it?

Parity with the normal room behaviour. Locally persist it in the appropriate storage layer

Have you considered any alternatives?

No response

Additional context

No response

[t3chguy]

Duplicate of #23196