It would appear that the speaker (or author) of this remark:
So your statement means that the person concerned had eaten the
previous day, possibly several times, but has not consumed any food
is referring to a statement of yours issued at some time in the past or relating to events that took place at some time in the past. How do we determine this?
The time phrase the previous day never means yesterday. "The previous day" always refers to a day farther in the past than yesterday.
To judge from the speaker's use of the phrase the previous day, your statement cannot have been issued today, and it cannot be about events that took place today. However, that logical conclusion conflicts with the present perfect, "but has not consumed any food since then", which treats your statement as if it were one made just a moment earlier.
The presence of the previous day explains the past perfect had eaten -- the consumption of food was an action that took place in a past time which is earlier than your statement, or earlier than the events it mentions. The time of your statement or the events it mentions is the reference time in relation to which the eating is being situated in time.
My guess is that someone doesn't understand the meaning of the previous day, either that, or is misusing the present perfect. If the speaker/author of the remark quoted above understands the implications of the previous day, the remark would have said ... and had not consumed any food since then.