After double checking, this appears to already exist, but the autodiscovery tag is slightly incorrect. So, I'm re-categorizing this as a bug. The feature already exists in 7.6, but doesn't quite work properly.

Here's the docs for autodiscovery: https://github.com/dewitt/opensearch/blob/master/opensearch-1-1-draft-6.md#autodiscovery

Currently, DSpace already generates an OpenSearch servicedocument. It's available at:
[dspace.server.url]/opensearch/service.

However, the HTML header includes an autodiscovery tag which is slightly incorrect. It looks like this on our demo site:

<link href="https://api7.dspace.org/server/opensearch/search/service" type="application/atom+xml" rel="search" title="Dspace">

There are two issues:

• the href URL is incorrect (correct URL would be https://api7.dspace.org/server/opensearch/service for the demo site)
• the mime type is wrong (correct type would be "application/opensearchdescription+xml" per the spec)

So, the correct link tag should look like this:

<link href="https://[dspace.server.url]/opensearch/service" type="application/opensearchdescription+xml" rel="search" title="Dspace">