Running your file past the AA 2019 Amplitude Statistics window shows that AA believes the extract contains 7 "possibly clipped samples". I wonder if these are what you are perceiving as the buzzing? Certainly, the specific syllables are slightly unpleasant to listen to, along with the rather too obvious "room tone/noise" on the whole recording.
So the first thing I did was to remove that noise, by using the gap in the speech to create a noise print in iZotope RX7 Advanced (yes, not AA but, IMO, by far the best tool for this work) and then processing the whole file with that noise print. I then used another module from RX7, the De-Clip (with a threshold of - 1.0 dB) to remove (what I hope is) your "buzzing". You can download the processed file from https://my.pcloud.com/publink/show?code=XZO6k97ZMmT3a6El0J8eoYFuO3XKQHJHLwNk
HTH, but perhaps it may not since it was "created" using software you may not have nor be able to purchase because, although it is excellent at what it is designed for, it is not cheap!
Having sort-of got the internet back at last, I've listened to it, and I'm not convinced it's an equipment issue at all. Sounds to me remarkably like a good mic is actually showing you how your voice projects forward - which isn't necessarily how you will perceive it. Actual buzzes tend to get louder when excited more, and you're saying that this one happens when you get quieter - that's a big clue.
Get the mic a bit off-axis and possibly slightly above mouth level, make sure you've only drunk clear fluids and have another go. Chances are you'll find a position where this isn't so apparent, and that's far more likely to be when you aren't facing the mic directly. Post-production fixes are expensive, and if you can get rid of the need for anything like this at recording time, that's definitely the way to go. Also, unless you are deliberately going for a bass-heavy sound, get slightly further away from the mic. TLM103's are excellent spoken-voice mics, but they can be depressingly revealing!
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