Brave New World made light of all the high stakes in the film, including how valuable Adamantium is. Granted, the plot centered around multiple factions trying to get their hands on a sample, but the significance fell to the wayside when international warfare came up. Nevertheless, the precious metal plays an even more influential role moving forward.
Whoever uses the prize turns the tide, plain and simple. The nation or faction doesn't matter—the individual who weaponizes the Adamantium—will make the difference. Fans have seen how powerful it is in Wolverine's hands. Picture what it'll do for villains like Omega Red, Romulus, and Cyber. They don't exist in the MCU—at least not yet—but renegades like them could equip themselves with Adamantium weapons, potentially changing the course of the Sacred Timeline. It's worth mentioning that the first vigilante brandishing one might not be an unknown.
After watching Sam Wilson (Anthony Mackie) have his Vibranium suit torn to shreds, piece by piece, he deserves an upgrade. An entire outfit comprised of the otherworldly substance isn't feasible when considering the weight factor, but wingtips are. Fans tend to forget that Logan gets weighed down by the excess Adamantium coating his bones, which is problematic for average humans.
As for Wilson, he'll probably commission a pair of wings—and perhaps a Red Wing shell. They might seem insignificant, but it's a mental tactic as well as a practical one. Consider how mercenaries and vigilantes walk into fights with Wolverine. They're aware of his metal claws ripping through flesh like butter. Sam Wilson could make the same impression on his foes in the scenario that he's gifted a pair of blade-like wings.
The other possibility is a pair of gauntlets. Wilson is a more hand-to-hand type of soldier, kind of like Steve Rogers. Gauntlets wouldn't be very expressive onscreen, which diminishes the use of Adamantium slightly. Of course, being a more tactical type of hero, Wilson might find a use for a pair of metal gloves that can absorb gamma radiation.
Keep in mind, though, that the forged version doesn't exist yet, meaning its abilities are yet to be determined. The sample gathered in Brave New World was the raw material. It'll take some time before a lab refines the metal into a shiny new claw. No one's saying Wolverine is first, though odds are tests will quickly conclude that the metal is best used as a slicing tool. Afterwards, the ball will keep rolling. The craze to acquire Vibranium in Wakanda Forever is a perfect example of the world's lust for power. The same thing is going to happen once people realize how useful its counterpoint, Adamantium, is.
Captain America: Brave New World is currently in theaters everywhere.