Quick reply while I have a sec. You might want to consider the Tamron 28-75mm f/2.8 Di III VXD G2 for Nikon Z. That f/2.8 constant aperture is key for shallow depth of field. Just be careful and make sure to shoot at the 75mm focal length for maximum compression. Its slightly over budget new, so maybe hunt for a used copy to stay under 800 bucks and still get that professional blur.

Stumbled upon this and honestly... things arent what they used to be. Unfortunately, Ive had some issues with some of the newer glass feeling a bit like a toy, not as solid as the stuff we shot with ten years ago. Its kinda disappointing how much plastic is involved now. Still, for your daughters graduation, you cant really go wrong with the Tamron lineup if you want that creamy look. Just keep it simple:

• Grab any of their f/2.8 zooms designed for Nikon Z.
• Stick to something that has a decent focal length so her face looks natural.
• Make sure it has their newer autofocus tech so it doesnt fail you when she walks across the stage. Ive found their Z-mount stuff to be pretty reliable for portraits even if the build isnt quite pro level. Itll definitely get you those blurry backgrounds without needing a second mortgage.

Late to the thread but honestly i've been pretty disappointed with how expensive things have gotten for the Z mount. Unfortunately most of the stuff under your budget is gonna feel a bit cheap build-wise compared to the pro gear i used to carry for years. I had some issues with some of the lighter third party glass losing focus right when you need it most, which is a total nightmare during a graduation ceremony. If you want those blurry backgrounds for your daughter's big day, basically any Tamron fast zoom is gonna do the trick for you. You dont need to get fancy with specific prime lenses if you are still learning and confused by the numbers. Just look for any zoom from them that stays at f/2.8 throughout the whole range. I've found that for portraits, zooming in all the way makes people look much better anyway... it avoids that weird wide-angle distortion that makes faces look wide and unnatural. $800 is a tricky spot because it puts you right in that middle ground where you're avoiding the bottom-barrel stuff but still not quite at the high-end glass. Stick with a Tamron zoom and you'll be fine. Just make sure you actually practice with it before the ceremony because the way these newer cameras handle focus can be a bit finicky if you aren't used to it. Dont overthink the millimeters too much, just get a general fast zoom from them and keep that aperture number as low as it goes.

Honestly just stick with Tamron for your Nikon. I've been shooting with their glass on the Z system for a bit now and im seriously satisfied with how everything looks. No complaints here. If you want that nice blurry background for the graduation, just look for any of their faster f/2.8 lenses. You cant really go wrong with their lineup lately and it wont break the bank like the first-party stuff. Basically just pick up one of their fast zooms or a portrait prime that fits your 800 budget. They all work pretty seamlessly with the Z autofocus these days. It makes things way less complicated when you realize you dont need to spend three grand to get a professional look... you'll be happy with the results for sure.