Okay, so if I'm following all these interactions properly:
- Wielding two Light weapons lets you make an extra attack with one of those weapons as a bonus action (no bonus damage from your ability modifier).
- The Nick weapon mastery (found on scimitars, among other things) lets you make the extra attack granted by Light as part of the same Attack action, freeing up your bonus action.
- The Two-Weapon Fighting fighting style feat lets you add your ability modifier to damage for the extra attack from Light.
- The Dual Wielder feat, in a change from the playtest, now makes no mention of the extra attack from Light, instead it simply allows you to make an extra attack as a bonus action with a melee weapon that isn't two-handed, as long as you attacked with a Light weapon.
- Extra Attack obviously lets you make extra attacks with the Attack action.
- The new rules for weapon swapping appear to handwave drawing and stowing, letting you do both as part of an attack.
So, if you have two scimitars, you would normally be able to attack twice as part of the Attack action (because Nick), plus however many Extra Attacks you have. If you then take Dual Wielder, you can attack again with your bonus action. If you have TWF, you get to add your ability modifier to the damage, but only for the attacks you make with the Attack action (Dual Wielder doesn't interact with TWF). In theory though, you could swap out your scimitar for a longsword and actually use it with two hands (it's versatile, not two-handed, technically) for 1d10 damage, rather than the 1d6 of a rapier.
Of course, a longsword isn't finesse, so you'd have to be Strength-based to get the maximum efficiency from this combo, and invest a whole feat in it. It would seem more efficient to just do fewer attacks that add your ability bonus to the damage, rather than construct your entire build around getting an average of 2 points of extra damage per turn.
A level 5, Str 20 scimitar fighter with DW and TWF would (without Action Surge) do three attacks at 1d6 + 5 dmg, plus an extra cheeky longsword attack for 1d10 dmg. Average = 29 dmg.
By contrast, the same fighter with a greatsword would make two attacks at 2d6 + 5 dmg, for 24 dmg, but would also have two additional feat slots, one of which could be Great Weapon Master which adds a flat +6 dmg bonus and lets you attack again if you kill an opponent.
I guess the scimitar/longsword blender is more useful for crit fishing, but it's a pretty marginal gain imo.