Jon Josep Thank you for clarifying the above.
My understanding is that you are trying to copy an elastic pool database to another logical server within the same subscription and same resource group, the Portal will not show the available Elastic Pool depending on the tier etc
If the source Elastic Pool is Business Critical while Destination is General Purpose. This is not supported during copy.
It will only work if the Destination is Business Critical. Same for General purpose.
In conclusion, you can only copy individual DBs but then it needs to be within the same tier.
After copy, you can change the service tier of the destination DB, or if you copied into a pool, then the entire pool's service tier can be changed. You can't just change an individual DB within a pool to a different service tier.
Regards,
Oury