What is the future equivalent of the word "Heritage"?

Posterity, while less common than "legacy" according to Google Ngrams, has been increasing steadily in usage since the 1960s and provides a more exact rhetorical parallel to "heritage".

Usage examples:

For-profit publishers like HarperCollins or Hachette don’t perform the kind of work required to preserve a cultural posterity. Publishers are not archivists. They obey the dictates of the market. They keep books in print based on market considerations, not cultural ones.

• Maria Bustillos, "Publishers Are Taking the Internet to Court", The Nation, 9/10/20

Over the last four decades, David Lynch has created some of the best-known and widely discussed screen works of our time. This distinctive writer-director’s art bears not only the mark of box-office success but also critical acclaim and cultural posterity.

• "Catching the Big Fish: Meditation, Consciousness, and Creativity," davidlynchfoundation.org

Iron Butterfly’s only (and dubious) claim to cultural posterity is 1968’s overwrought, absurdly long ”In-A-Gadda-Da-Vida,” which inexplicably appears on Light and Heavy: The Best of Iron Butterfly only in a three-minute single edit.

• Ira Robbins, "Light and Heavy: The Best of Iron Butterfly," Entertainment Weekly, 3/5/93

In response to talk from those working on the institutional side of things, about the desire for access to everything that goes into a work, about the need to catalogue as many aspects of its creation as possible for the sake of institutional and cultural posterity, Carlson demurs, “I hear something like, ‘we have to capture what we can’ from an institution, and I get more and more protective – of the dancers in the union, of our presenters, of the artists working on the production. When you’re commissioning a piece, there are opportunities for conversation with the living artist, to include them in the decision-making about what to include in the ‘catalogue’. If that conversation about documentation is in place before the actual event occurs, you’ll have a lot less push-back later, not to mention the opportunity to establish something greater than you’d have done without the artist’s insights.”

• Susannah Schouweiler, "Cataloguing performance: Opening the kimono - how much to reveal and to whom?" walkerart.org, 11/10/11

The scope and volume of Rudes’ work is impressive by any standard, all the more so since Tuscarora is critically endangered. If a lexicon even half as rich could be produced for every endangered speech form, the benefits to linguistics and to the world’s cultural posterity would be magnificent in the extreme. This monumental work seems destined to become the authoritative source on the Tuscarora lexicon and morpheme inventory, and should definitely be acquired by any scholar or library interested in Iroquoian linguistics or cultural heritage.

• Edward Vajda, "The Uralic Language Family: Facts, Myths, and Statistics," Canadian Journal of Linguistics, January 2003.

Legacy

anything handed down from the past, as from an ancestor or predecessor: the legacy of ancient Rome.

Second definition: https://www.dictionary.com/browse/legacy