It's mine by rights" would be more on the lines of speaking for the group as a whole
Nah, it means exactly as it seems. Its an option to imply its yours personally with assumption its already bound to you. The writing treats it that way.
Here is what happens if you give the Prism to the commander Therezzyn - this exact cutscene plays no matter what if you pick those options - you pull it out of your pocket and it jumps back to you as if its bound to you personally, but even after this cutscene it will be in Shadowheart's inventory still. It does not make sense. Please dont rationalize and suggest that the scene would play the same way if the writers assumed its in Shadowheart's possession. This is another example of writing being insufficient - a cutscene and dialogue just doesnt exist to account for situation where you dont have it but Shadowheart does, even though it seems it's fairly easy to find yourself in this situation.
I also reloaded the save after the Prism and exhausted dialogue options with Shadowheart and there's nothing about the artifact, just the regular options about the relationship. I was able to trigger the dialogue you describe by getting the Chosen scene in goblin area without Shadowheart around.
The same sequence also plays regardless of which character you initiate dialogue with, as you see in this example the person isnt actually playing Laezel origin, he just decided to initiate as Lae'zel because there are some differences in how youre treated in the Creche if you initiate as githyanki (its not specific dialogue for Lae'zel)
