Answer
Check whether your ADFS server is missing a Service Principal Name (SPN) registration — a missing SPN on the domain controller is a common, specific cause of integrated/'sign in as current user' authentication failing with a 401 even when manual-credential SSO login works and the rest of the ADFS configuration looks correct. Adding the required SPN(s) to the domain controller (for example, via the Windows setspn command) resolves this specific failure mode.