WordPress Design Refinement

Overview
I have an existing WordPress website for a nonprofit summer camp. The site is functional, but I need design refinement and layout cleanup to achieve a calmer, more established look.
I am not looking to copy code or migrate another site.
I will provide a reference website for design inspiration only.
The goal is to recreate the design feel (spacing, hierarchy, restraint, color balance) using my existing WordPress setup.
Scope of Work (Punch List)
A. Global Header & Navigation (All Pages)
Add a top utility bar
Left: phone number
Right: Facebook & Instagram icons
White text/icons on green background
Update main navigation styling:
Background: cream
Menu text: brown
Keep existing fonts
Subtle hover behavior (no dramatic color changes)
Style one menu item (Support) as a button
Blue background, white text
Rounded corners
Only menu item styled as a button
Fix mobile menu behavior:
Menu should slide in from the right or dr...