Variant searches often blend several different questions: what variants exist, which one is rarest, how luck affects them, whether they earn more, and how much to bid. Only the first question is answered by the current official description. Treating the entire cluster as verified would overstate the evidence.
Luck upgrades are part of the official high-level game loop, but the public information checked for launch does not list costs, levels, effect sizes, or odds. That means a break-even calculator or gacha simulator would need invented constants. The site keeps those tools on hold until reliable or reproducible data exists.
The practical launch approach is to use variants as a collection-evidence label, not a numeric tier. If you observe a clean income difference for a particular character and variant in your own session, you can test that number in the auction calculator. Keep the confidence label honest because one observation may include other changes.