Don't download 200MB of JS for a JavaDoc search feature that most people don't use

### Upcoming End-of-Support

- [X] I acknowledge the upcoming end-of-support for AWS SDK for Java v1 was [announced](https://aws.amazon.com/blogs/developer/announcing-end-of-support-for-aws-sdk-for-java-v1-x-on-december-31-2025/), and migration to AWS SDK for Java v2 is recommended.

### Describe the issue

When visiting https://sdk.amazonaws.com/java/api/2.25.67/software/amazon/awssdk/regions/providers/DefaultAwsRegionProviderChain.html

I observed that the loading spinner on the tab seemingly spun forever. After looking at the network tab, I saw it was downloading this: https://sdk.amazonaws.com/java/api/2.25.67/member-search-index.js

It's 216MB of JS... I'm pretty sure this file is generated by the default JavaDoc tool. It's a search index which I think is only useful when using the top-right search box, which I never use anyway.

I don't know whether Chrome refuses to cache it because it's so massive, or cache headers are not set properly, but every single page requests it from scratch.

The type search at https://sdk.amazonaws.com/java/api/2.25.67/type-search-index.js is also 17MB which is less horrendous, and at least that one gets cached, but that is still too much to download.

For now, I blocked this URL `https://sdk.amazonaws.com/*search-index.js` in my ad blocker

### Links

https://sdk.amazonaws.com/java/api/2.25.67/software/amazon/awssdk/regions/providers/DefaultAwsRegionProviderChain.html

As well as every single page