Answer
RMB > Properties > Read Only writes the setting into your own Personal Profile, which is why it only affects your own session. To make a field read-only for a defined group of users, apply the Read Only setting to the shared Base Profile(s) those users are attached to instead, so everyone inheriting from that Base Profile gets the restriction. To make it read-only for absolutely every user, including the Application Owner (who isn't affected by profile-level settings), define it as a Conditional Field instead — a framework-level condition that enforces the restriction independent of any user's profile.