The “season flag” is dictated by the “Date First Published” value (aka, first_release_on column in the products ingestion template). Change that value to a date in the near future and the season flag will change to "Soon!"
In the example below, the “Date First Published” for the given product is 2024-01-01 (Jan 1, 2024).
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For exact definitions of the Seasons, navigate to the admin Season Seasons page (Admin > Management > Other > Seasons).
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2024-01-01 (Jan 1, 2024) falls within the “new” product release season. On the public site, the “public label” of “New!” would be displayed as the season flag.
By changing the “Date First Published” value to 2024-03-01 (Mar 1, 2024), the product would fall within the “upcoming” product release season. On the public site, the “public label” of “Soon!” would now apply.