I meant something like Washington DC's OPC[1]. Note that these commissions are not themselves perfect; they're typically limited in authority to "recommendations," which the police (or DA) may still ignore.

However, to answer the following (which isn't what I meant, but I think is interesting):

> but assuming it’s a private firm would you not have the same criticism that it’s not a neutral third party and is biased towards whoever hired them?

I think the answer to this is similar to the answer found in arbitration: arbitration is typically performed by a well-known firm, and that firm is obligated through contract to perform fair proceedings. In other words: there are civil penalties on the table if the independent party does not execute their job fairly.

That being said, I think an unrelated but still governmental investigation arm would be sufficient here.

> What is the role of a state level investigation bureau if not to investigate state-level issues involving state agencies?

You can find the GBI's services listed here[2]. They have a lot of responsibilities, most of which aren't tied to investigation of local police. I think it'd even be fair to say that they aren't particularly equipped to investigate local forces.

[1]: https://policecomplaints.dc.gov/

[2]: https://gbi.georgia.gov/services

Patterns of Gunshot Residue Gunshot residue (GSR) may be deposited by two mechanisms: (1) impact deposition from particles propelled by the force of the blast, and (2) fallout deposition of drifting particles that settle on a surface. Persons close to the blast, specifically the shooter, will likely have GSR from impact. Bystanders are likely to have GSR particles from fallout. Shooters are more likely to have a greater number of particles than bystanders, but not always. Settling of airborne GSR may take up to 10 minutes following firearm discharge. The depostion of GSR particles following initial firearm discharge is primary transfer. However, secondary transfer of these particles to other surfaces can occur from contact with the surfaces or persons on whom the particles have deposited, as with handshaking or contact with clothing. Movement of persons following the shooting, or even scene investigation by forensic scientists, may alter GSR distribution. Further tertiary or even quaternary transfer is possible. Law enforcement personnel may carry particles from prior shooting events. (Blakey et al, 2018)

The amount and pattern of GSR deposited may vary by the gun used to fire the bullet. Most GSR emanates from the ejection port of a semiautomatic pistol. GSR is expelled from the gap between cylinder and frame of a revolver. There is greater particle number with revolvers than with automatic rifles. Particle numbers are greater with nonjacketed bullets, mainly due to an increase in particles composed of lead. A faster burning rate of propellant powder reduces the distance of GSR particles travelled. (Blakey et al, 2018) (Vachon and Martinez, 2019)

GSR may be expelled from the firearm ahead of the bullet, along with the bullet, and following after the bullet. Though the amount of residue deposited tends to decrease with increasing range of fire, the actual deposits can be highly variable for ranges up to 20 cm.(Brown, Cauchi, et al, 1999) GSR has been reported to be found at distances from 6 to 18 meters forward of the shooter, and up to 6 meters laterally. However, climatic conditions significantly influence recovery rates for GSR. (Dalby et al, 2010) Use of atomic force microscopy (AFM) for detection of particle size in relation to range of fire has been described. (Mou, Lakadwar, and Rabalais, 2008)

https://webpath.med.utah.edu/TUTORIAL/GUNS/GUNGSR.html