Since at least 2011, iPhone offered the hotspot. That was in the near pre-sim trimming days...
If you still have the old phone, it may have the capability, but not the "feature". Some carriers blocked the hotspot option.
Your iPhone SE could have that same issue depending on the original carrier. The functionality is there, but the option may be hidden. If the hotspot feature doesn't appear on the unlocked iPhone SE, follow these instructions:
To set up Wi-Fi hotspot for an Apple iPhone SE
From the home screen, tap Settings. ...
Tap Cellular.
Tap Personal Hotspot. ...
Tap the Personal Hotspot switch to enable it.
Tap Wi-Fi Password.
Enter a password, then tap Done.
The personal hotspot is now active allowing other devices to connect via Wi-Fi.