I noticed the "Extract Data Task" screenshots also show a "Raster Format" parameter, and set to "ESRI GRID". ESRI GRID is an old format, and could be finicky with file paths, especially things like spaces or special characters, that you should avoid. Is the "Raster Format" parameter actually used in your case? If so, maybe trying to switch to another raster data format might help.
Secondly, I see in one of the screenshots, just before the other "Failed" messages, a "Consolidation Failed" message. I see some other messages about e.g. lack of disk space on the drive where consolidation of data takes place, or the consolidation process not being able to find the data involved, in this older thread:
https://community.esri.com/thread/56303
The link above also in one of the posts there, points to a setting that is also in ArcGIS Pro (Go to Options/Share and Download in Pro), where you can set where to "consolidate" the data before publishing. Maybe trying to set this folder to another drive (it defaults to your user profile which may be resource limited in your organization), and using a shorter path, may help.