I've always had a problem integrating Goliaths into my settings because their niche is already stuffed with more interesting races, like orcs, barbarian humans, mountain dwarves, true giants, and so on; we don't need another vaguely northern mountainy furs-and-leathers barbarian race.
So what if we lean into their odd designation as Lawful Neutral, and the origin of their name, and make them more like Babylonians and ancient Canaanites. There isn't really a rigidly lawful player race; Dwarves are called that, but they're more about tradition than the Law. In D&D, law can cover tradition (dwarves), rigid militant and government structures (hobgoblins), codes of stewardship (tritons), and legalism (which doesn't quite have a PC race yet).
Imagine a race of half-giants with a deep seated code akin to Hammurabi's, and shift their competitiveness and combativeness to ritualized, legalistic dueling and militant challenges. You know, like the Biblical Goliath.
Their aesthetic is the clay slab, from cyclopean architecture to tablets. Rectangular, towering, brutalist and utilitarian.
Also, they're big gamers, not just athletes, loving their big awkward mancala boards. Any form of competition, from sports to gladiation to card games to the court of law is the goliath's domain, and they're big on rigid, obeyed rules and fair play (as in canon). Despite their legalism, they desire plainness of speech and abhor sophistry; if a legal code can't be displayed in full in the public square, it will be viewed as suspicious, even potentially diabolic.