Draw Stream Binning Rasterizer is not being used yet in the open drivers yet. Enabling it would be mostly in the amdgpu kernel driver but optimizing performance with it would be mostly in radeonsi and game engines.
HBCC is not fully enabled yet, although we are using some of the foundation features like 4-level page tables and variable page size support (mixing 2MB and 4KB pages). On Linux we are looking at HBCC more for compute than for graphics, so SW implementation and exposed behaviour would be quite different from Windows where the focus is more on graphics. Most of the work for Linux would be in the amdgpu kernel driver.
Primitive Shader support - IIRC this is part of a larger NGG feature (next generation geometry). There has been some initial work done for primitive shader support IIRC but don't know if anything has been enabled yet. I believe the work would mostly be in radeonsi but haven't looked closely.
For both DSBR and NGG/PS I expect we will follow the Windows team's efforts, while I expect HBCC on Linux will get worked on independently of Windows efforts.