When you are on a server with hardcore=true, you will not see the different HP textures above your hotbar and you will not see the "Spectate world" or "Leave server" buttons on the death screen. You will still be put into spectator if you click "Respawn"

How to reproduce: 
1. Open Minecraft 1.13
2. Launch Minecraft Server 1.13 with hardcore=true
3. Look at your hotbar. Your HP will remain as if you were not in hardcore.
4. Die in the game. The death screen will show "Respawn" instead of "Spectate World" and "Title Screen" instead of "Leave Server."
5. If you click "Respawn, you will still go into spectator mode.