Vectorise AI-Generated Logo

I have a finished logo that was created with an AI tool and is currently only available as a raster image. Before I send it off to be printed on T-shirts, mugs and other merchandise, I need a crisp, fully-editable vector version.

Your task is to reproduce the artwork exactly as it appears, preserving every shape, gradient and, importantly, the existing colour palette from the supplied file. Minor tweaks that improve print quality are welcome, but the overall look and feel must remain unchanged.

Deliverables:
• Clean, well-organised vector artwork created in Adobe Illustrator (or comparable software)
• Final files supplied in AI, EPS, SVG, CRD and print-ready PDF, all on a transparent background
• Paths optimised—no stray points, embedded images or unnecessary effects

I’ll choose the freelancer whose experience with similar logo conversions is clear, so please highlight that in your message. Quick, precise turnaround is appreciated.