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I'm trying to understand the Noise Reduction implementation in Audacity and I was wondering how the Frequency Smoothing is implemented.

Frequency Smoothing (bands): At values of 1 or higher, this control spreads the noise reduction into the specified number of neighboring bands. This modifies the signal you were intending to keep, but if artifacts remain in the noise-reduced audio the smoothing can make those artifacts sound more acceptable. There is a chance that smoothing will make the desired audio less clear, so where your desired signal is strong and of wide frequency range and the noise is light, try leaving this control at 0 (off).

Source: https://manual.audacityteam.org/man/noise_reduction.html

So my question, how does it mathematically spread the noise reduction gains into the sidelobes? Would it not interfere with the other gains for the other bins?

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