I have removed the white noise tones from the 17 audio files with white noise present by using Audacity's Notch Filter effect to cut out the frequencies of these tones. These tones were likely an unintended production mistake, potentially caused by electrical interference in the studio space. This method isn't as ideal as working with the original source project files, but from comparing the original audio to the edited files, the two files sound identical to me apart from the removal of the high pitched sound.

This has only been tested with the steam version of Planescape Torment: Enhanced Edition but should work with other versions.

Installation Instructions:
Extract 'override' folder to the Project P base folder.

Previously in trying to find a fix for this online, I found that some people weren't able to hear the high pitched sound. With that in mind I should state this mod isn't essential, and if you can't hear any white noise in game there is no need to download it. For an example, you can listen to the audio in this video I uploaded as an example of the white noise in game: 
https://www.youtube.com/watch?v=oqRS2MkoMy4

For myself, and hopefully for others too, this mod makes the game playable again, as the constant white noise was making my ears hurt.

Thanks to user 'kjeron' on the beamdog forums for listing which WAV files they could hear a white noise in! 
it meant I didn't have to listen to all ambient sound files myself to find ones with a white noise tone.

This mod edits these .WAV files found in the game's .bif files:
AR_0102
AR_0108
AR_0109
AR_0201
AR_0505
AR_0507
AR_0509
AR_0512
AR_0607
AR_1405
AR_3004
AR_3005
AR_3008
AR_3013
AR_3013D
AR_CURST
AR_TENT6

I potentially may have missed audio files with white noise in them. If I have, please let me know in the comment section.

Enjoy!

5th of November 2023 update
Here are the steps I took to make this mod if you want to recreate it yourself. You can also download
the unmodified extracted files from this mods download section and skip straight to editing these files in Audacity.

Download Near Infinity from https://github.com/Argent77/NearInfinity/releases (I use the setup-win file)
to extract the games problematic .WAV files

Open chitin.key in Near Infinity, which is located in the base folder of Project P. Locate the .WAV files
mentioned earlier in the WAV folder. You can also locate these files using Near Infinity’s search function.
Extract these files as WAV, not as original. Extracting the files as original extracts audio files that don’t play, at least for me

Now open the file or files you have extracted in Audacity. In Audacity I used the Notch Filter, which you can find in the effects tab.
I selected the entire track and applied the Filter at 6200hz, with a Q value of 5.0.
This frequency and Q value varies per file though, as the white noise varies in frequency and size across the 17 files.
This is where you can experiment, trying higher or lower values for those two settings to your liking.
My goal was to modify the files to remove just the white noise, without affecting anything else about how the audio sounds

Lastly export these files as .WAV. While they are now modified, .WAV is a lossless format, meaning there is no quality loss.
Place these files in the ‘override’ folder in Project P. If there isn’t an override folder create one.
To test this in game you can start a new save file, and see if you can hear the white noise when you
first enter gameplay in the morgue.
 
Other people might say to use WinBiff or InfExp but I’ve had no luck with them. WinBiff crashes
frequently and when I extract a .WAV it doesn’t play. InfExp asks for a .ini file in the game directory,
something that was probably removed with the enhanced edition of Planescape Torment.