This already exists if you know what to look for, and are willing to dive into a technical solution.
The bleep tone is usually a 1kHz sine wave (according to wikipedia). We can simply create a band pass filter that removes all 1kHz tones from the audio output of windows.
This does have side effects. Most notably that human speach, especially some female voices, are around this 1kHz frequency too. Since the tone was designed to mask voices, this makes sense. So I’m not sure if the side effects are worth it, but you can certainly try.
Creating such a filter on live audio can be done with something like this: https://github.com/AndreasArvidsson/WinDSP
Never tried it before myself, but the description matches exactly what you would need. You will want a PEQ filter with a high Q and significant negative gain around the 1000Hz frequency. I’m not an audio engineer, so I have no idea what values would work well. But if you want to play with those: a higher Q creates a narrower band around the 1000 to filter out.
Just chug a glass of olive oil.