Multi-Step Appointment Booking Form Development

I need a multi-step booking form for our website that integrates with our appointment booking system's API.

Requirements:
- The form should have 5 steps
- The steps would be:
Who you are + address on first page
Choose type of service on second page + Extras
When and how often on page 3
Extra information + comments on page 4 (all optional info)
Payment details + Discount code + cancellation policy on final page

- Must connect seamlessly with our existing booking system's API. Our booking system is Launch27 and has an API you can connect to. Their API doc is here: https://bitbucket.org/awoo23/api-2.0/wiki/Home

Other features we would like for this form:

- Our Google Reviews/rating somewhere on the page to trust/enforce our good reputation
- Some general selling points on the page too
- Lead capture - if a customer fills in their contact details and email but does not book, have their contact details sent to a mailchimp campaign
- I would like the form to be as smooth and pretty as possible.

This company has a similar form so we can use this as inspiration: https://urbanmop.ca/book-now/form/

Our current booking form is here: https://www.maidtoclean.com.au/book-now

Ideal Skills:
- Experience with API integration
- Strong knowledge in web development
- Good UI design
- Previous work on multi-step forms

Looking for a developer who can deliver a smooth and user-friendly booking experience.