AFAIK the Bitbucket Server Integration plugin does not explicitly support Configuration as Code, but at least unclassified.bitbucketPluginConfiguration.serverList can be set. (It is separate from unclassified.bitbucketEndpointConfiguration.endpoints used by the Bitbucket Branch Source plugin.)

IIRC, the problem with not having it configurable via JCasC is that the plugin requires a shared secret when creating a consumer. However, you can't use any existing credential as a secret and instead you have to manually create one in the UI in the plugin configuration. This means that if you manually configure this plugin but use JCasC, the secret you create will get obliterated the next time that JCasC runs. I don't know why it can't use a built-in credential but it effectively makes this plugin useless if using JCasC. We opted to just use generic webhooks and live with not having the build results available in Bitbucket.

Doing some testing, I found if you install the plugin, you can set the credentials in JCasC like this:

        - bitbucketToken:
            id: "bb_token"
            description: "LAN Bitbucket"
            secret: "my_secret" 

After some more searching and testing, I found you can just use a REST API call to Bitbucket to send the build information and skip using this plugin altogether:

 curl -X "POST" "https://bitbucket.example.com/rest/api/1.0/projects/myproject/repos/myrepo/commits/<commit_id>/builds" \
     -H 'X-Atlassian-Token: no-check' \
     -H 'Content-Type: application/json; charset=utf-8' \
     -u 'my_username:my_password' \
     -d $'{
  "key": "my_jenkins_job_key",
  "state": "SUCCESSFUL",
  "url": "https://jenkins.example.com/job/my_jenkins_job_key/<build_id>/",
  "parent": "my_jenkins_job_key"
}'

For some undocumented reason, the API won't store the status unless the "parent" is set as well as the "job_key" even though the docs don't mention this at all.

I was able to add the Bitbucket server to Jenkins via JCasC using the unclassified.bitbucketPluginConfiguration.serverList key. but I cannot leverage JCasC to add the Application Link (Oauth consumer) and seems like doing it manually from the web UI is the only option. 

It would be great if this support is added to the plugin. Some organizations (including mine) have a 100% as-code requirement for all Jenkins configs and this throws a wrench in that.