https://www.qualcomm.com/products/mobile/snapdragon/smartpho...
810 had a 64-bit core designed by ARM
https://www.qualcomm.com/products/mobile/snapdragon/smartpho...
820/821 had a 64-bit Kryo custom core designed by Qualcomm
https://www.qualcomm.com/products/mobile/snapdragon/smartpho...
After that it was all cores from ARM. The custom CPU team worked on their server chip before getting cancelled and most of the team went to Microsoft
865 (2019) has Cortex-A77 + Kryo 4xx Silver 888 (2002) uses Cortex-X1 + Cortex-A78 + Cortex-A55 cores
Snapdragon 865 has standard Arm cores. The same is true for the older Snapdragon 855, Snapdragon 845 and Snapdragon 835, which I am using or I have used in my phones.
The claim of Qualcomm that those cores have been "semi-custom", is mostly BS, because the changes made by Qualcomm to the cores licensed from Arm have been minimal.
https://www.qualcomm.com/products/mobile/snapdragon/smartpho...
I worked on it in 2014. The table does have 808 listed. That may have been a lower end version.
Qualcomm got caught being late. They were continuing development of custom 32-bit cores and Apple came out with a 64-bit ARM core in the iPhone. The Chief Marketing Officer of Qualcomm called it a gimmick but Apple was a huge customer of Qualcomm's modems. Qualcomm shoved him off to the side for a while.
https://www.cnet.com/tech/mobile/qualcomm-gambit-apple-64-bi...
Because Q's custom 64-bit CPU was not ready the stop gap plan was to license a 64-bit RTL design from ARM and use that in the 810. It also had overheating problems but that's different issue. There were a lot of internal politics going on at Q over the custom cores and server chips that ended up in layoffs.