You can reapply the pattern by using the Apply Symbology From Layer tool. The Input will be your results and for the Symbology Layer navigate to wherever your install is ... \ArcGIS\Pro\Resources\ArcToolBox\Templates\Layers\Emerging_All.lyrx (for ArcGIS Pro. For ArcMap, use the .lyr file).
That being said ... losing the symbology whenever you close a project and the fact that the output is being sent to the Project tab and not the TOC are not expected behaviors ... they sound like they may be set-up issues? You might reach out to tech support.
Hope this was helpful!
-Jenora