How do I categorize cash that I contribute to my business to cover bills the business needs to pay?
As a small business owner, it is understandable that periodically you contribute your personal cash to cover your business bills, etc. This cash inflow into the business is categorized as a loan. You're loaning your company cash and eventually, the company will pay you back. You would categorize this cash that you contribute to the "Owner’s Loan" account.
If you and other investors are contributing cash/capital as part of your cap table (investment in your company in exchange for shares or an ownership % stake in your company), then this would be "Owner’s Equity". This is because the investors who contribute $ are now owners in your company.