Imagine a race of intelligent humanoid beings standing almost 2m tall with 2 trunks instead of arms for handling and gripping objects, these trunk-like arms are similar to the elephant's except they can't smell or siphon water. They have co-existed with the neanderthals and us amicablely since the dawn of tool making but lately there has been some tensions arising from scarcity of food, I want to pit them against one another for the title of apex predator in the same timeline like early bronze age in this universe. Here the neanderthals were driven to extinction by the cunning humans so its us and the trunk-arms, what melee weapon can they forge and how can they fully utilise it in a brawl with us? Can they use a sword or an axe effectively and as acrobatically as a skilled human?
This will probably be about the limit of what they can make with their trunks.
They don't have tusks or the bulk of an elephant. They will also be limited by lack of digits and a thumb. Making a sword will be much harder than wielding one. First they would have to invent mining, fire, bellows, leather trunk gloves and so on. Imagine sewing gloves with a trunk!
Here you see a real elephant wielding a stick as a weapon. Notice that it doesn't use the fine control at the nose end of the trunk. Its natural grip is to wind the trunk around the stick.
Video of an elephant confronting a rhino with a stick
The elephant uses psychology to outwit the rhino rather than striking it. This tactic wouldn't work against humans, especially if the trunk people are their own size.
Sadly I think the trunk people will be wiped out first (love the idea though!), just leaving us and the "thals" to battle it out.
Depends on the tip of the trunk
The trunk of an african elephant has two finger-like extensions
So the lack of digits and an opposable thumb could be compensated for, as a pincer grip would be possible. Though this probably isn't as efficient as actual hands and digits.
If you consider Asian elphants' one digit trunk, then a club is probably the right answer.
Stone tools should be accessible to your trunk-armed humanoids
Your premise suggests that your trunky guys have access to stone tools and weapons, as they had a friendly relationship with neanderthal and us. Moreover, a two-digits trunk tip seems enough to create and use basic stone tools, as well as making spears.
So in this case, at least stone-tipped spears, stone axes, and probably a bow and arrows.
The difference in technology might not mean certain win for us
At that point, I would wonder more about the difference in strength and versatility trunks bring, as opposed to arms. Your trunk-boys towering over everyone else at 2m tall is another factor. If a trunked-armed man can lift 150kg with one trunk, how far and how deadly could he throw a spear? He may be able to use bows and arrows more effectively than us, and more range seems better than a melee weapon made of bronze.
I'm expecting those guys to win every arm wrestling competition, though we would need an expert's point of view regarding the actual strength a trunk can muster. Those trunk-arms are a weapon by themselves.
Intelligence matters more
This, was considering intelligence similar to our own, and a technological level equivalent before the "break-off" between the species, right before bronze usage came in play. If the trunk-people are not intelligent enough to use their 4 fingers creatively to at least adapt what others invented, or are not smart enough to use their trunk's forte effectively, then they are surely doomed. Otherwise, I'ld probably bet on them (though this should be nuanced regarding reproduction rates, life expectancy, energy consumption and so on)
I do think they should be able to create bronze weapons, but that is my personnal opinion, and it is your choice as the author to determine their level of intelligence and adaptability. Heck you could have them use their better physical prowess to force the other species to make weapons for them, if you want