Should we have a sitemap for better SEO?

Should we have a sitemap that better links to all rooms in the room directory?

Otherwise, search engines will have to crawl the paginated list on the homepage for thousand of pages and the sort/order isn't stable since it just relies on room member count.

I assume the sitemap would just include rooms from a select few homeservers we specify.

Dev notes

/robots.txt pointing to a sitemap

Sitemap: https://s3.amazonaws.com/some-bucket/prod/sitemap.xml

User-agent: *
Allow: *

sitemap.xml (this is based on the Gitter sitemap)

<?xml version="1.0" encoding="UTF-8"?>
<sitemapindex xmlns="http://www.sitemaps.org/schemas/sitemap/0.9" 
      xmlns:mobile="http://www.google.com/schemas/sitemap-mobile/1.0" 
      xmlns:image="http://www.google.com/schemas/sitemap-image/1.1">
      
      <sitemap>
        <loc>room-url</loc>
      </sitemap>
      <sitemap>
        <loc>room-url</loc>
      </sitemap>
      <sitemap>
        <loc>room-url</loc>
      </sitemap>
      
</sitemapindex>

https://developers.google.com/search/docs/crawling-indexing/sitemaps/build-sitemap suggests a different format

Start by tracing how the room directory and homepage expose room URLs, then review the proposed /robots.txt and sitemap.xml formats. Determine how the selected homeservers and rooms should be represented and where the generated sitemap can be served. Done means robots.txt points to a valid sitemap that lists the intended rooms for search engines.