According to Airbus when they responded to leehamnews.com in 2019, the A321neo required flare law changes that are unrelated to the bigger engine, and the modified laws were in response to customer requests based on conditions discovered in simulator sessions.
The origin of the "excessive pitch" is associated to a reduction in efficiency of the angle of attack protection in a very remote combination of conditions, these being: The need for the crew to perform a dynamic manoeuver (such as a go around) AND the aircraft being below 100ft AND specific landing configuration AND a very aft CG. [emphasis added]
— Bjorn's Corner: Airbus' A321neo has a pitch-up issue (now with a second update). July 19, 2019. leehamnews.com.
While the article does not specifically mention the higher flare mode activation, this at least confirms flare-law differences that apply only to the A321neo.