I'm self-employed with a small business. Should I report business expenses if I had no income in 2022?

Yes, you should report your business exactly as it is.  However, I will caution you that you must have a motivation and a plan to make a profit.  At some point the IRS will deam that you don't have a business and it is just a hobby.

Thanks. I understand. Is there a downside if I don't report expenses?

No downside, other than perhaps paying more taxes. The IRS is concerned with unreported income, not expenses.