Update search docs to recommend Pagefind over Algolia

.cspell.yml

@@ -37,6 +37,7 @@ words:
   - nate
   - nvmrc
   - Obasi
+  - Pagefind
   - subpages
   - techdocs
   - toolkits

docs/search.md

@@ -10,8 +10,9 @@ sidebar: { label: Search }
 This page describes some common alternatives for static site search.
 
 - [Google search](#programmable-search-engine-by-google)
-- [DocSearch by Algolia](#docsearch-by-algolia)
+- [Pagefind](#pagefind)
 - [Lunr](#lunr)
+- [DocSearch by Algolia](#docsearch-by-algolia)
 
 ## Programmable Search Engine by Google
 
@@ -31,23 +32,26 @@ website.
 
 - Search index is completely managed and hosted on Google servers.
 
-## DocSearch by Algolia
+## Pagefind
 
-[DocSearch](https://docsearch.algolia.com/) is a search tool powered by the
-Algolia search engine that crawls your docs and provides a dropdown search
-experience on your website.
+[Pagefind](https://pagefind.app/) is an open source search tool for static
+sites. It indexes your built site as a post-build step and serves search results
+directly from static assets.
 
 ### Pros
 
-- Provides Front-end widgets out of the box: search input, dynamic positioning
-  of search results, etc.
-- Integrations with popular frameworks
-- Support for multi-language search.
+- No hosted service or third-party search provider required
+- Works well with static site generators
+- Free and open source
+- Support for multi-language search
+- Fetches index data on demand, which helps it scale better than fully
+  in-browser indexes
 
 ### Cons
 
-- Not entirely free- Limited to 10k records
-- Limited access to features.
+- Requires a build step to generate and update the search index
+- Search is limited to content available in the built site
+- UI customization may require some JavaScript and CSS work
 
 ## Lunr
 
@@ -70,10 +74,32 @@ needing external, server-side, search services.
   Docsy, this should be _very_ easy to setup).
 - Depending on site setup, may require javascript knowledge
 
+## DocSearch by Algolia
+
+[DocSearch](https://docsearch.algolia.com/) is a search tool powered by the
+Algolia search engine that crawls your docs and provides a dropdown search
+experience on your website.
+
+### Pros
+
+- Provides front-end widgets out of the box: search input, dynamic positioning
+  of search results, etc.
+- Integrations with popular frameworks
+- Support for multi-language search
+
+### Cons
+
+- Search index is managed and hosted on Algolia servers
+- To use the free DocSearch program, you must apply and be approved
+- The free DocSearch program requires displaying the "Search by Algolia" logo
+- Less control over indexing and search behavior than self-hosted options
+
 ## When Is It Best To Use One Over Another?
 
 If you are looking to create a search capability for your open source project
-without having to depend on a 3rd party service, then you should consider using
+without having to depend on a third-party service, then you should consider using
+[Pagefind](https://pagefind.app/) first. If you need a more custom
+implementation that runs entirely in the browser, you can also consider
 [Lunr](https://lunrjs.com/). You can take a look at
 [this custom implementation](https://github.com/vitessio/website/pull/1119) or
 [Hugo/Docsy implementation](https://github.com/etcd-io/website/pull/403) to see