How it works, and what to trust
SecretSlices uses Shamir's secret sharing. Each share is a point on a random curve whose shape is the secret. With the required number of points the curve is known; with even one fewer, every possible secret of that length is exactly as likely as before. That is a mathematical property, not an encryption that could be broken later. The one thing a share does show is how long the secret is; tick Hide the secret's length to blur that too.
Recovery is checked. A share that was mistyped is reported by its number. If the shares do not fit together (one was changed, or belongs to a different secret), you get an error, not a wrong secret. This applies to shares that start with ss1.; shares made by earlier versions of SecretSlices can still be recovered here, but they cannot be checked, and the page says so when it reads them.
Nothing leaves this page. It is a single file with no outside resources, and its security policy forbids every network request, so even a bug could not send your secret anywhere. It saves nothing in your browser either. What you copy or download does go to your clipboard and your disk, and the secret is on your screen while you work, so use a device you trust. For the highest assurance, save this page, disconnect from the network, and open the saved file.
What it cannot do. Anyone holding the required number of shares can read the secret. Someone you give a share to can refuse to return it, so create more shares than you require. If one person hands you a complete set of shares, you are trusting that person: shares are not signed.