I have questions about the deliverable. What will be the desired application of the logo? Is this request for resolution/scaling purposes, or are you planning on printing? Your image has gradients which are possible to do in .ai, but may not give you the best print results. It can build it however you'd want, but it may be worth looking simplifying the gradients into solid spot colors. I can promise you it can still look really good.
For the vector part, you are looking at 2 options. Retracing software, which is cheaper with so-so results. This is an example:

I would recommend a re-draw personally, which would be a lot higher quality. That type of service would be around 5k FG. It takes a lot of time.
Hopefully that helps.
This post was edited by Traceofred on Dec 5 2022 03:22pm