Question about the activations keys for DR 16 and DR 17

Hello. I have bought 3 Pocket 4K and each one of them included a serial (for two computers) from the Davinci Studio.
Driven by the desire to go from Final Cut to Davinci Resolve I already used a code for two of my macs, and today I have used another one on a different mac (total 3 computers)
The fact is that when the program started (after entering the key) it invited me to upgrade to Davinci 17. I have done so and it has asked me for the key again. I have entered it and then I have seen that the key could no longer be used.
I thought that the password was for the equipment and that it would work for the DR 16 or the DR 17 but I did not imagine that I would lose both uses of a single password on the same equipment in a matter of minutes ...
I do not know if I explain myself very well.
I am using google translator and I am not sure if I am expressing myself correctly.
I'm worried about this and also thinking that if I update the other two Macs to 17 I will run out of key uses ...
If I had known, I would have directly installed the DR17 without going through the DR16.
Thank you very much in advance.
Greetings!
Driven by the desire to go from Final Cut to Davinci Resolve I already used a code for two of my macs, and today I have used another one on a different mac (total 3 computers)
The fact is that when the program started (after entering the key) it invited me to upgrade to Davinci 17. I have done so and it has asked me for the key again. I have entered it and then I have seen that the key could no longer be used.
I thought that the password was for the equipment and that it would work for the DR 16 or the DR 17 but I did not imagine that I would lose both uses of a single password on the same equipment in a matter of minutes ...
I do not know if I explain myself very well.
I am using google translator and I am not sure if I am expressing myself correctly.
I'm worried about this and also thinking that if I update the other two Macs to 17 I will run out of key uses ...
If I had known, I would have directly installed the DR17 without going through the DR16.
Thank you very much in advance.
Greetings!