The formality levels are stressing me out already

It is a smaller deal than the textbooks make it, and yes, foreigners get a lot of slack. Here is the version that matters in practice.

What you actually need on arrival: one politeness level. The 해요 form. It is polite, it works with strangers, shopkeepers, teachers, older people and classmates, and nobody will ever be offended by it. That is the whole survival kit. Textbooks present four or five speech levels as if you need them all on day one; you need one.

What happens if you get it wrong: essentially nothing. Koreans do not expect foreigners to navigate this, and the reaction to a learner using a slightly wrong ending is usually amusement or approval that you tried. The people who get judged on formality are Koreans, in Korean social hierarchies, with real consequences. You are not in that system and everyone knows it.

The two things that do matter, and they are behavioural rather than grammatical:

1. Use two hands when giving or receiving something to someone older — money, a card, a glass. Costs nothing and is noticed.
2. Do not use 반말 (casual form) with someone older or a stranger until they offer. This is the one line worth respecting, and it is easy because you will not know 반말 for months anyway.

On age: you will be asked your age early and often. It is not nosiness — it establishes how people should speak to each other, and Korean has no comfortable default until that is settled. Answer it plainly.

The honest reassurance: the students who arrive most worried about this are usually the ones being most careful, and being careful is the entire requirement. Learn 해요, use two hands, be visibly making an effort. That covers you completely for the first year.