You can't normally add a button (in HTML language), but you can add a link and stylize it as a button.
To add an extra link to the main menu, log in as admin, and move to Pages tab, and you can add extra links there to point to any page or external website.
To stylize a link like a button and to create an icon in front of it, it requires some CSS jobs.
Each extra link will have a CSS class like this:
.qa-nav-main-custom-1 .qa-nav-main-link
.qa-nav-main-custom-2 .qa-nav-main-link
.qa-nav-main-custom-3 .qa-nav-main-link
.qa-nav-main-custom-4 .qa-nav-main-link
......
An icon can be a special Unicode character, a codepoint in conjunction with a specific font, or an image.
Example:
.qa-nav-main-custom-11 .qa-nav-main-link::before {
content: "pets";
color: crimson;
}
qa-nav-main-link::before {
font-family: "Material Icons";
font-size: 24px;
position: absolute;
}