As an interesting note, even the basic premise of the preceding comment is not accurate. A small but increasing number of heart transplants are performed as DCD operations, which means the donor's heart stops naturally on its own before being removed: https://www.acc.org/Latest-in-Cardiology/Articles/2022/11/21...
It is technically possible to artificially keep the heart beating during the transplant process, but that's a very recent technical development and a much more difficult surgical procedure. So stopping the heart first is normal.
That means that your grieving next of kin have decided (for you, since you no longer have conscious thoughts) that your last act on this planet will be an act of kindness. You will give your heart, lungs, eyes, etc to someone that can still make use of them. The last thing you will do, is saving the life of someone.
So yes, they (directly or indirectly) stop the heart.
And that is a good thing.