Problem definition

Due to deprecation of 2LOi application link on Cloud, Jira Service Desk on server cannot utilize knowledge base found on Confluence Cloud instance (which can be also concluded from here: Update: Knowledge bases must be on the same domain as your service desk).
Modifying application link to use "OAuth" (withoug impersonation) makes knowledge articles non-searchable, which means this functionality does not work anymore.

Suggested resolution

Develop a mean of integration that would enable Service Desk server users to use Confluence Cloud knowledge base again.

Notes

The functionality does work if "OAuth" is being used in the link configuration and if Confluence Cloud is configured to be used with Anonymous access.