When you add a web link to a Jira Cloud issue pointing to an Azure Devops work item Jira will embed some of the Azure Devop info like the status.
The only thing you need to do is authenticate in Azure Devops with OAuth so this looks like an out of the box Jira feature.
Example:

I have 2 questions:
- When can I find any documentation about this behavior?
I'd like to know what other types of links are supported
- Any chance this is available on Jira Data Center? When I test this it does not work but I'd like to find a feature request in JAC