You flew it as an assignment so, no, it won’t appear in your recents.
No, LOL is the 2nd assignment. The 1st (22 days ago) was GTASA.
Time is irrelevant. If you flew it as a result of an assignment, then it won’t appear. You can of course find it using coordinates and fly it independently – that will make it appear in your recents (I think).
That would probably work for a banner/marketing image, but it would be too small for an icon. Good idea, though
The thing I’m glad about is that I didn’t restart my progress at WC after downloading the patch. I was about to face Yolk Star™ at wave 50.
SPeaking of Yolk Star at the previous WC Yolk Star was at wave 50 too, it had 4 laser guns, but at this WC it had 5 although it’s still the same wave meaning it’s the same diff, did the diff got buffed at this update or it is intended?