There’s nothing to it. The daily objectives just doesn’t trigger that you have reached General; and at present there is literally no benefit from acquiring stars on top of it.
However, I believe that TC did mention in a fairly recent stream that they have plans for excess stars after players reach General. I didn’t see the stream myself but someone else mentioned it. No clue what these plans are though.
Scrap is a good idea. But having said that, TC would really need to expand on the Supply Drop items because there is genuinely nothing in it that I want. We received 3 characters early on which were craftable, but nothing since then. My scrap is just building up gradually and not being used. I’d gather just play the game to build up Horde/Escape skills.