Redesign Header Menu On ecommerce Website

Hello,
Please see attached a screenshot of the current website menu, also the menu in action here:
https://www.jvd.me.uk/ (under PRODUCTS)

As you can see, the products have been broken down into 4 categories, however, as the range has increased, it has become quite cluttered and unorganised.

The task is to scrap this current design and recreate it, carefully planning, to ensure the best, user-friendly layout.

1) We would like to include some vector images, to illustrate the types of products/categories.

2) We would like to include a 'search' box, and possibly 'filter' settings, into the design, so that users can easily find what they're looking for.

You will be required to look very carefully and give much care, attention, and thought to the design, ensuring that you fully understand what is required, and more importantly, know exactly what products are available, so as to be able to offer the best possible solution.

Please take a detailed look over the website, which offers a vast selection of doors, windows, and roofing products, available in many styles, colors, and types.

NOTE: The existing branding, styling, coloring etc... must be kept.

The main categories are as below, however, this is not set in stone, or to say how the design is to be followed, just for added reference.

Any questions, please feel free to ask.

...Commercial...
Aluminium Commercial Doors
Steel Doors
Steel Louvre Doors
Steel Louve Panels
Steel Acoustic Doors

...Residential...
Everything else

...Also, there are...
Front Doors
Back Doors
French Doors
Patio Doors
Bifold Doors

...Windows...
Casement
Sliding
Bay/Bow
Flush
Tilt & Turn

...Roof...
Lanterns & Lights

Thanks
Chris.