

## Plan: Add clickable "try it" icons to search tips

### Challenge
The chat widget is a third-party embed loaded via `widget.js`. To inject a search term into its input, we need to find the input element inside `#chatsku-widget` and programmatically set its value and dispatch an input event. Since the widget uses `data-embed="inline"` (not an iframe), its DOM should be accessible.

### Implementation Steps

1. **Add a helper function** `injectSearchTerm(term: string)` that:
   - Queries `#chatsku-widget` for an `input` or `textarea` element
   - Sets its value to the provided term
   - Dispatches `input` and `change` events so the widget reacts
   - Scrolls the widget into view

2. **Refactor the search tips list items** to include a small clickable arrow icon (`ArrowRight` or `CornerDownRight` from lucide) next to each tip's search term. Each icon calls `injectSearchTerm()` with the relevant term (e.g., "Plexiclass", "pipes", "Do you have a 2 inch stainless steel ball valve for high pressure?").

3. **Add a tooltip** on the icon saying "Try this in the widget" for discoverability.

4. **Switch the active tab to "widget"** when a tip is clicked (in case the user is on the Admin tab). This requires lifting the tab state to a controlled `Tabs` component with `value`/`onValueChange`.

### Search terms mapped to tips
- Spelling correction: `Plexiclass`
- Synonyms: `pipes`
- NL query 1: `Do you have a 2 inch stainless steel ball valve for high pressure?`
- NL query 2: `I need safety glasses that are anti-fog for my warehouse`
- NL query 3: `What schedule 80 PVC pipe do you carry in 1 inch?`

(Voice Input tip has no clickable icon since it's mic-based.)

### Risk
The widget's internal DOM structure may not expose a standard input element, or may use shadow DOM. If so, the injection won't work and we'd note that limitation. We can add a fallback that copies the term to clipboard with a toast message.

