Status symbols vs decoration
Historically, jewelry performs two distinct roles - ornamental and decorative, and also as a way of displaying status. Precious metals and gemstones fulfilled both roles effectively, as they are scarce, highly visible (shininess helps), and also gold and silver are easier to craft into intricate decorations than harder metals while at the same time more long-lasting than decorations made from organic materials. Scarcity is a prerequisite - for example, in some gold-abundant cultures we have seen that e.g. feathers of rare birds fulfilled a similar role to gold jewelry in Europe.
Already now these roles have somewhat diverged for jewelry, as various cheap materials are excessively used for decorating our bodies while at the same time various visible non-jewelry items have taken some 'marketshare' of status symbols away from jewelry - high-end electronics, brands of clothing, shoes and handbags, flashy cars.
Artificial scarcity to replace real scarcity
In order for something to work as an effective status signal, it must actually correlate with status - i.e., it must be hard for a low-status person to show it. One way for easily replicable items to keep fulfilling the role of status symbols is to keep them scarce by non-technical means.
In modern world, a prime example where this already works is branded items - a Luis Voitton handbag can be replicated rather cheaply, but trademark laws restrict the making and sale of such items. This allows them to keep functioning as effective status symbols, being easily distinguishable from otherwise similar off-brand items that are cheaper and thus don't indicate status.
In your world, if producers/designers of jewelry can make visually distinct styles of jewelry that are then legally protected, then this will allow jewelry to 'keep on living' and fulfilling a similar function as high-end luxury brands do today. This requires a world where some things that technically can be duplicated by 'atomic makers' are prohibited to replicate or distribute - perhaps not the best case for consumers and society, but entirely plausible given current economic and legal trends.
Possible restrictions on showing off
Historically, this has often been solved by legislation - e.g., medieval cities mandating that specific clothing, colors, jewelry, etc. could be worn only by specific classes of people, and visually 'disguising' yourself as another class/caste/etc was a crime.
In certain times and places a rich merchant wouldn't be allowed to wear, say, a purple cloak - and in this case those who could do it had it as essentially a piece of jewelry, an obvious visible status symbol. In some societies the right to wear a sword or a symbolic dagger also esentially fulfilled this function, as fighting decreased and it went from a often used defense item to a simple inconvenience that still shows membership of a better social class.
In the same manner, a future world - assuming it becomes more socially stratified and less egalitarian - could easily restrict types of jewelry to certain groups of people. Others "could" replicate them but simply wouldn't be allowed to wear them in public; and this fact would make it desireable for the higher classes to use that jewelry just to highlight that they can and distinguish themselves from the commoners.