Settings UI should remember its search upon reload

[sbatten]

Issue Type: Feature Request

Some settings require reload and this may be in the middle of the user modifying settings. It would be cool if the settings UI could remember the search through reload.

[roblourens]

#58499

I would say "the search should be persisted when reloading with the settings editor open".

[roblourens]

PR welcome.

• Use getEditorMemento to cache the search string of the settings editor (settingsEditor2.ts)
• Implement setVisible, the state should only be cached or restored if the settings editor was visible when the window reloaded.

[roblourens]

Besides the search string, this should also cover the scroll position of the settings list per #57365. If that turns out to be hard, it can be a separate PR...