How long does a hard inquiry stay on credit report?

It doesn't affect much. Even if it has an affect, you will have to compare options to take out credit cards, any loan, or a mortgage.
So, you don't have to worry much. Just check that the companies should take your consent before doing the hard inquiry, so that you're aware how many queries are being made and during which period.

Hard inquiry stays on credit report for 2 years and it affects your credit score for 12 months only. Usually, you get a hard inquiry when you apply for a credit card, student loan, or a mortgage.

If you apply for a credit card or home loan, you will get a hard inquiry. It stays for 2 years. It usually affects your score for 1 year. Are you looking for a new credit card ? Why are you asking this question?

Multiple hard inquiries within a 45-day period is regarded as a single inquiry. It is true that it affects your credit score negatively a bit, but you don't have to worry about it much.
However, make sure the inquiries are made within the mentioned timeframe.