Docs search needs improvement

### Describe what's missing in our docs

Search on the docs site doesn't reliably find me what I need. I typically have to use a combination of docs search and Ask Kestra AI to find something in the docs (unless I know exactly what page it's on already).

When searching for "defaults" I wanted to find a specific info box I'd seen before, but didn't remember where it was. I searched for both "defaults" and "default" but never found the page I was looking for - https://kestra.io/docs/tutorial/inputs#defining-inputs

> The plural form defaults is used instead of default for two reasons. First, default is a reserved keyword in Java, so it cannot be used. Second, this property allows you to set default values for a JSON object which can be an array that simultaneously defines multiple default values.

Additionally, the Ask Kestra AI seemingly can't see the info box? Here is an example conversation:

Start by reproducing the docs-site searches for “defaults” and “default” and inspect the linked tutorial page at /docs/tutorial/inputs#defining-inputs. Compare the results with what Ask Kestra AI can access from the quoted info box; done means the relevant page is discoverable and the info box is available to the AI.

Written by the indexing model from the issue text.