docs: improve next/image localPatterns error page (#89914)

Align with https://nextjs.org/docs/messages/next-image-unconfigured-host

Closes:
https://linear.app/vercel/issue/DOC-5850/feedback-image-configuration-it-doesn-t-work-my-pattern-is-defined-as

errors/next-image-unconfigured-localpatterns.mdx

@@ -4,11 +4,26 @@ title: '`next/image` Un-configured localPatterns'
 
 ## Why This Error Occurred
 
-One of your pages that leverages the `next/image` component, passed a `src` value that uses a URL that isn't defined in the `images.localPatterns` property in `next.config.js`.
+One of your pages that leverages the `next/image` component, passed a `src` value that uses a local path that isn't allowed by the `images.localPatterns` configuration in `next.config.js`.
+
+Each part of the `src` value is matched against your `images.localPatterns` definitions:
+
+- **Pathname**: The path must be covered by your glob pattern, e.g. `/**` or `/assets/**`. Single `*` matches a single path segment, while double `**` matches any number of path segments.
+- **Search**: If specified in a pattern, it must match the full search string exactly (including the leading `?`). Globs are not supported for search.
+
+If any of these differ from the actual `src`, the image will be rejected.
+
+Common pitfalls that cause this error:
+
+- A too-narrow pathname pattern (e.g. `/assets/` instead of `/assets/**`).
+- Setting `search: ''` when your images include query strings like `?v=123` or `?t=timestamp`. An empty string means only URLs **without** query strings are allowed.
+- Forgetting that pathname patterns are case-sensitive and must match exactly.
+
+See the [Local Patterns](/docs/pages/api-reference/components/image#localpatterns) reference for details.
 
 ## Possible Ways to Fix It
 
-Add an entry to `images.localPatterns` array in `next.config.js` with the expected URL pattern. For example:
+Add the pathname to the `images.localPatterns` config in `next.config.js`:
 
 ```js filename="next.config.js"
 module.exports = {
@@ -22,9 +37,43 @@ module.exports = {
 }
 ```
 
-Omitting the `search` will allow all query strings.
+### Any search params (default)
 
-If you want to prevent the query string from matching, you can use the empty string, for example:
+To allow any search params, omit the `search` key:
+
+```js filename="next.config.js"
+module.exports = {
+  images: {
+    localPatterns: [
+      {
+        pathname: '/api/images/**',
+        // search is omitted, so ?v=123, ?t=456, or no query string are all allowed
+      },
+    ],
+  },
+}
+```
+
+### With specific search params
+
+To allow only a specific search param value:
+
+```js filename="next.config.js"
+module.exports = {
+  images: {
+    localPatterns: [
+      {
+        pathname: '/assets/**',
+        search: '?v=1',
+      },
+    ],
+  },
+}
+```
+
+### No search params
+
+To disallow query strings entirely, use an empty string:
 
 ```js filename="next.config.js"
 module.exports = {