I think some of the posters are missing your point. Logically you know you can't have limitless babies, you already have four so you're well aware of what it takes and the challenges of adding a new baby to the family.
None of the typical "focus on your existing children", "the world doesn't need more people" are actually answering your question of how to let go of your heart's longing to have another.
I don't know the answer to this as I have three and would love another. Four has always been the number I wanted. But I know if we do have a fourth I will be so incredibly sad and emotional about it all. It's actually putting me off deciding because I know I will also be deciding to have my last baby.
For me, the idea of this incredibly intense but so precious stage of my life being over is overwhelming. Motherhood has been transformative for me so to say goodbye to ever becoming a mother again will be incredibly hard.
I have enjoyed my pregnancies, I have been lucky enough to have experienced what it is like to have a wonderful birth, I've loved breastfeeding my children. While I'm incredibly excited to watch my children grow up it will still be hard to say goodbye to this part forever.
I asked my own mum for advice and she said that even if you never feel done eventually you do feel at peace with it. I think I will need to take some time to really sit with it and let myself feel all the emotions before I consider trying for our fourth.
Best of luck OP, I really hear what you're saying. It's ok to feel sad about it all.