lichmaster
Hero
IMO these count as different rules to compute how many melee attacks you can make with the Attack Action. As for AC calculation and similar, you choose which to apply, but you can't apply both.It's likely an oversight that Thirsting Blade wasn't written as Extra Attack. Otherwise, I could go say Fighter 5/Warlock 5, and get both Extra Attack and the additional attack from Thirsting Blade, depending on how you read it.
If Thirsting Blade was conceived to synergise well with Extra Attack and multiclassing in general, I think it would have simply stated that you are considered as having the Extra attack feature.