External ssd not booting even though it says it is the boot drive on settings

I recently bought an external ssd for my iMac 2013 so I could use it as a boot drive however it doesn't seem to work.

Firstly I formatted the SSD to MacOs extended journaled and carried out internet recovery. It didn't work so I then used Carbon Copy Cloner to copy my internal drive to my SSD and then set my external SSD as the boot drive however that didn't work as it booted up from the internal drive.

I'm pretty sure it booted up from the internal drive as:

1. I tested the speed and it is the same as my internal drive and no where near the speed of the SSD.
2. I can also see the SSD in my finder.
3. I can use the Mac without the external SSD being connected.
4. in disk utility I can carry out a first aid on my external SSD and the system is still responsive, yet when I try to carry it out on my internal drive it says the system will be unresponsive which makes me think that the internal drive is being used to boot up the system despite settings telling me that my external drive is being used.

I'm really confused to why it is booting up on my internal drive when in the settings it says my external ssd is being used. Any suggestions? Thanks.