Recreate & Expand Existing Logo

I already have the registered logo in a single JPG and now need it professionally rebuilt so it can serve every real-world use case. The artwork must stay true to the current colours and proportions, yet be polished to a classic and timeless standard for future-proof brand guidelines... (Budget: €250 - €750 EUR, Jobs: Adobe Illustrator, Adobe Photoshop, Branding, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Design)