To access age-gated parts of Discord, you need to verify your age. This sounds reasonable. It's not much different to having your id card checked when purchasing alcohol. Actually it's better as you only have to do it once, not on each visit.
In the case of an online-based ID check, even with nice looking privacy terms, there is no guarantee that your ID won't be stored forever and/or re-analyzed many times cross-checking with other services, and worse leaked.