The curse does give additional damage each time your Eldritch Blast, weapon attack, spell, etc., damages a target. So at say Warlock level 11, your Eldritch Ray does d10 + 2d4 from your archetype curse + d6 if you have Hex also running, and you get three such ranged ray attacks at the target on your turn.
Likewise, if you have Thirsting Blade (which I assume counts as Extra Attack) and are two-weapon fighting, then you'd have four attacks (2 main hand + 2 off-hand) that each benefit from + d4 damage form the Archetype curse at Warlock level 5. I'd be tempted to play a two-weapon fighting Warlock with Pact of the Blade, Life Drinker, Thirsting Blade, and Devouring Blade (level 12+, gives 2 extra attacks rather than one, from the 2024 Player's Handbook), to have 5 attacks at level 12+ inflicting this extra damage. I will note that the 2024 PHB reduced the extra damage from Lifedrinker, instead of adding the spellcasting ability modifier to damage, it adds +d6 damage and allowing you to spend a hit die to recover HP. That said, Warlocks tend to be glass cannons in melee combat, and that's a high investment in eldritch invocations to make it so effective.
