Should foreigners in Korea open a bank account and get a phone number first?

Question

Hello! It's been two months since I arrived in Korea, and I have a concern these days.

I am currently living in Itaewon and I received my Alien Registration Card (ARC). So, I went to a mobile phone store to register my phone number under my name. But they said I need a bank account. So, I went to a nearby Hana Bank, and this time they said I can't open an account without a phone number. What is this, really? Lol

Does anyone know what I should do first in this process? I'm a bit confused by these situations as a newcomer to Korea. Any advice from those who have had similar experiences would be greatly appreciated!

From what I've researched, some banks have stricter procedures for foreigners. Is there a way to open an account without a phone number? Or should I try a different approach?

I would really appreciate any help!