Broken "search" in Settings menu

### Prerequisites

- [x] I am running the latest version of ComfyUI
- [x] I have custom nodes enabled

### What happened?

The search bar in Settings does not work properly. If I want to change the node ID badge visibility for example, I should be able to type "badge" in the search bar and see all settings items that contain the word "badge".
Instead, I just get api price badge.

### Steps to Reproduce

1. Open settings menu
2. Type any search term and press enter
3.

### How is this affecting you?

Feature doesn't work as expected

### ComfyUI Frontend Version

1.41.2

### Browser

Chrome/Chromium

### Console Errors

```javascript

```

### Logs

```shell

```

### Additional Context

_No response_

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-9097-Broken-search-in-Settings-menu-30f6d73d36508134b82fcd26beae3006) by [Unito](https://www.unito.io)

Start by reproducing the issue in the Settings menu using “badge” as the search term, then locate the frontend code responsible for filtering settings items. Confirm the fix by checking that all settings containing the term appear after searching, including the node ID badge visibility setting.

Written by the indexing model from the issue text.