Just a quick note - the Assign button will appear as it’s own option in topics/posts and won’t be under the menu
I just tested it on my end on a TL3 account set under the following conditions and got these results:
So…with this being said, you’d need to set trust_level_0 as @Moin suggested. I think it would be expected to work otherwise if you selected everyone, so maybe this is a bug?