Sorry for the incomplete information.Given that the CPU has 24 lanes total. 4 to the chipset, 4 to the PCIe Storage and 16 to the motherboard PCIe Slots
1 slot will be 16, its highly unlikley that the second 16 slot is electrically 16. Or maybe it is 16 - but shares lanes with Slot 1. In which case the GPU will get 8 and the second slot will get 8 (if something is inserted, otherwise the GPU will get 16)
It might be supplied by the chipset, but my experience of those is that tend to be of a lesser standard. The two PCIe x1 are probably chipset
However I don't actually know as you didn't post what motherboard you had - which leaves me / us guessing.
But you should be OK with a X8 HBA with the GPU running in X8 as well.
It's a Dell Inspiron 5676. Doesn't list the motherboard in the specs. The chipset is AMD promontory X370.
As far as the PCIe slots go, your logic makes sense, all I can report is what I see and what is reported in the specs. I've attached the manual.