Has the bug, when turning on the processing effects and entering first-person makes the brightness level too high, been fixed?

Wow I didn't expect to see a MDE World Peace avatar on GOG, lol.

It depends on what you're holding in your hand, IIRC.

Picking up the syringe in the tutorial mission made difficult to see anything, so white.

(Contracts also has this issue when you hold the flower case in the hotel mission)

The broken lighting in first person mode has existed in the game since 2006. Io Interactive never bothered fixing it for whatever ungodly reason. The executable file is to blame, I think. From my experience, the Steam version doesn't have this issue at all, so I pasted Good Old Game's executable file into my Steam directory, and suddenly the excessive lighting manifested itself. One would think that Io Interactive could've easily patched the file before rereleasing it, but I guess that they're too busy with want-to-be James Bond now.

Has the bug been fixed yet?

fixed it!!!
by replacing the launcher with new one
heres link just copy then paste to hitman bloodmoney directory :

https://www.mediafire.com/file/bqxjd4s64l8jubj/HitmanBloodMoney.exe/file