This issue is goes back to the 5E D&D Player's Handbook. Thirsting Blade in A5E is the same as in the 5E D&D PHB. Multi-classing rules on page 164 of the PHB specifically state that Thirsting Blade and Extra Attack do not stack.
But yes, having an A5E designer chime in might be helpful, regarding whether Thirsting Blade should count as Extra Attack or not, specifically for two-weapon fighting two off-hand attacks, once you get Extra Attack. I.e., was that a design oversight or intentional, and would it be unbalanced to allow it.
All level 5 warlocks count as having extra attack by virtue of the extra blast feature.
They can* make two attacks with two-weapon fighting as long as they make at least one qualifying melee weapon attack with the attack action.