[code] icons of terminals are not preserved on reload

[JanKoehnlein]

Bug description

See microsoft/vscode#124359

This issue is a reminder we should adapt our RemoteTerminalChannelServer to correctly pick up the terminal's icon and remember it once that's fixed in VS Code.

Steps to reproduce

1. Open a new terminal and switch on Show tabs in the combo box to select the terminals
2. Change icon / title of the terminal
3. Reload the browser tab
   -> the tabs show as empty tree items, without icon and title

Expected behavior

Icon and title should be preserved.

Example repository

Any

Anything else?

No response

[JanKoehnlein]

Should be fixed via #4403