As of now there is no direct integration using which we can directly get Search Ad Campaign related data from Adobe Media Optimizer to Adobe Audience Manager but it is possible through adobe analytics.
Advertising Cloud is able to pass data in Analytics via our server to server integration for us to understand if the ad impacted the consumer to visit the website. For example, we can capture view-through data and understand if someone saw the display ad (delivered via Advertising Cloud) and then went to the advertisers' web page a few days later (via the Analytics pixel on the web-page), we can capture that as a view-through conversion and say the ad contributed to the person visiting the website. From there, Analytics can understand other ways users are interacting with the web page (bounce rate, page views etc.) to help create audiences to re-target, or build look-a-likes (via pushing Analytics segments into Audience Manager). Additionally, we can create audiences via Analytics data and push those audience segments into Audience Manager through server to server integration to house all segments in one place for
For more information on this integration,you can also refer to below link from advertising cloud community: