Short answer: you can't prove an idea is unpatented, but you can find out quickly whether close prior art exists. Here is the order we recommend.
Use Google Patents and USPTO Patent Public Search. Search for the function ("folds inward so the wet side is enclosed"), not your product name. Try 5-10 synonyms. Read claim 1 of anything close.
Open a close patent, note its CPC codes (e.g. A45B), and browse other patents in that code. Many matches use words you'd never guess.
"A smart water bottle" isn't what's patented; a specific combination of features is. Write down your 3-5 key features and check each against what you find.
Our report searches 9.7M US/WO patent families, then charts the 10 closest against your features with quoted text. It's a fast, cheap first look, not an exhaustive or legal search.
If the landscape looks clear, a registered patent attorney or agent can run a professional search and give a patentability opinion.
Not legal advice. Not exhaustive.