For "carving up" there are technologies like SR-IOV (Single Root I/O Virtualization).[2]
For advanced usage, like prototyping new hardware (host driver), you could use PCIem to emulate a not-yet-existing SR-IOV-capable GPU. This would allow you to develop and test the host-side driver (the one that manages the VFs) in QEMU without needing the actual hardware.
Another advanced use-case could be a custom vGPU solution: Instead of SR-IOV, you could try to build a custom paravirtualized GPU from scratch. PCIem would let you design the low-level PCIe interface for this new device, while you write a corresponding driver on the guest. This would require significant effort but it'd provide you complete control.
[1] https://qemu.readthedocs.io/en/v8.2.10/system/devices/virtio...
[2] https://en.wikipedia.org/wiki/Single-root_input/output_virtu...
Passthru or time sharing? The latter is difficult because you need something to manage the timeslices and enforce process isolation. I'm no expert but I understand it to be somewhere between nontrivial and not realistic without GPU vendor cooperation.
Note that the GPU vendors all deliberately include this feature as part of their market segmentation.
Serious work, detail intense, but not so different in design to e.g. Carmack's Trinity engine. Doable.