settings ui: Add text field support to ui layer (#37868)

This is an initial implementation that isn't used for any settings yet,
but will be used once `Vec<String>` is implemented.

I also updated the window.with_state api to grant access to a
`Context<S>` app reference instead of just an App.

## Example

<img width="603" height="83" alt="Screenshot 2025-09-09 at 2 15 56 PM"
src="https://github.com/user-attachments/assets/7b3fc350-a157-431f-a4bc-80a1806a3147"
/>


Release Notes:

- N/A

crates/settings/src/settings_ui_core.rs

@@ -43,6 +43,7 @@ pub struct SettingsUiEntry {
 #[derive(Clone)]
 pub enum SettingsUiItemSingle {
     SwitchField,
+    TextField,
     /// A numeric stepper for a specific type of number
     NumericStepper(NumType),
     ToggleGroup {
@@ -150,6 +151,18 @@ impl SettingsUi for Option<bool> {
     }
 }
 
+impl SettingsUi for String {
+    fn settings_ui_item() -> SettingsUiItem {
+        SettingsUiItem::Single(SettingsUiItemSingle::TextField)
+    }
+}
+
+impl SettingsUi for SettingsUiItem {
+    fn settings_ui_item() -> SettingsUiItem {
+        SettingsUiItem::Single(SettingsUiItemSingle::TextField)
+    }
+}
+
 #[repr(u8)]
 #[derive(Clone, Copy, Debug, PartialEq, Eq)]
 pub enum NumType {