I am just trying out Bedrock Server for the first time and am experiencing the exact same issue. Server and clients are on the same LAN, clients say sign-in is required.
Server is 1.16.201.2 for Linux
Clients tested are:
1.16.201 for Win 10 (from Microsoft Store)
1.16.201 for iPad
Let me know if I can provide any further information or do any further tests to help debug this.
Sorry, I believe this stems from a misunderstanding of how offline mode works. This issue BDS-5658 explains it.