“The have”: Sorry, never heard as an English learner of this.
If the sentence needs a subject, and it does, “Sie”, meaning “they” is necessary. “Sie haben” means “They have”: Yes, correct, plural 5. person conjugation.
This is the plural form of the definite article “the”: You are right that the article “the” can mean der/die/das/den.
But not only this.
We have to accept that single words can have multiple meanings; this also drives me often crazy in Portuguese grammar and translations
Then there is the Pronoun Derjenige/Diejenige/Dasjenige.
More Pronouns for “die”:
Which (die/welche), that (die, jener, welche), who (die, welche).
If you think about this different context and you finally drive away from “die” only being used as an article, it maybe gets more clear.
Well, my native language is hard to explain when I never had to formally study it on Duolingo or the German grammar somewhere else
I hope the other referenced article which irridmemorizza had linked could explain it a bit better.
Memrise is nice to review words and to see new (different) phrases/sentences examples in action which grammar you have at best formally learned elsewhere so you can finally recognize patterns and it makes “click”; but with grammar and missing explanations (there are no MEMS to select from in the offical 1-7 courses) it is important to have other resources in parallel.
www.lingvist.com (you can learn your first 3000 words for free) also has a grammar popup panel which you can show when you make an error. The grammar explanations and verb tense tables are longer…but you would need to take the time to read them so cram learning new words does not work as good.