Precise Logo Vector Conversion

I need a JPEG logo converted to a vector format. The proportions and text are already ok. I've included a picture that highlights important details and areas that need slight color adjustments. The vector logo will be used for physical products ranging from 2cm to 2 meters tall.

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It is important that the details and shading highlighted in the second picture with an outline are kept, the outlines are not to be kept, they are to illustrate the separate shading regions of the original file. The grey areas are to be black (202020 hex), the coffee is to remain the same, with care to keep the "shiny" portions, the yellow/gold colour of the wording can slightly be increased in contrast (a touch darker) and the two dots above the "i" and "j" can be a touch darker to better match the rest of the text.

I have already attempted this project before, I can send you a copy of that file to show what is not acceptable to me, I was not very clear the first time and the blame does not rest on the person I was working with.
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Ideal Skills and Experience:
- Proficiency in vector graphic software (e.g., Adobe Illustrator)
- Attention to detail for accurate conversion
- Experience with logo design and modification
- Ability to make precise color adjustments