How can I add engraved style to my buttons using CSS?

You can add button effects using box-shadow CSS. You can see an example here.

Here I added CSS file and the HTML code to demonstrate box-shadow property in css.

box-shadow: [inset?] [top] [left] [blur] [size] [color];

Here is HTML code,

<div class="buttons">
 <h1><code>box-shadow</code> Effect</h1>
 
 <button class="pulse">Pulse</button>
 <button class="close">Close</button>
 <button class="slide">Slide</button>
 <button class="fill">Fill In</button>
 <button class="up">Fill Up</button>
 <button class="raise">Raise</button>
 <button class="offset">Offset</button>
</div>

Here is CSS code,

/* box-shadow: [inset?] [top] [left] [blur] [size] [color]
*/
 .fill:hover, .fill:focus {
	 box-shadow: inset 0 0 0 2em var(--hover);
}
 .pulse:hover, .pulse:focus {
	 animation: pulse 1s;
	 box-shadow: 0 0 0 2em rgba(255, 255, 255, 0);
}
 @keyframes pulse {
	 0% {
		 box-shadow: 0 0 0 0 var(--hover);
	}
}
 .close:hover, .close:focus {
	 box-shadow: inset -3.5em 0 0 0 var(--hover), inset 3.5em 0 0 0 var(--hover);
}
 .raise:hover, .raise:focus {
	 box-shadow: 0 0.5em 0.5em -0.4em var(--hover);
	 transform: translateY(-0.25em);
}
 .up:hover, .up:focus {
	 box-shadow: inset 0 -3.25em 0 0 var(--hover);
}
 .slide:hover, .slide:focus {
	 box-shadow: inset 6.5em 0 0 0 var(--hover);
}
 .offset {
	 box-shadow: 0.3em 0.3em 0 0 var(--color), inset 0.3em 0.3em 0 0 var(--color);
}
 .offset:hover, .offset:focus {
	 box-shadow: 0 0 0 0 var(--hover), inset 6em 3.5em 0 0 var(--hover);
}
 .fill {
	 --color: #a972cb;
	 --hover: #cb72aa;
}
 .pulse {
	 --color: #ef6eae;
	 --hover: #ef8f6e;
}
 .close {
	 --color: #ff7f82;
	 --hover: #ffdc7f;
}
 .raise {
	 --color: #ffa260;
	 --hover: #e5ff60;
}
 .up {
	 --color: #e4cb58;
	 --hover: #94e458;
}
 .slide {
	 --color: #8fc866;
	 --hover: #66c887;
}
 .offset {
	 --color: #19bc8b;
	 --hover: #1973bc;
}
 button {
	 color: var(--color);
	 transition: 0.25s;
}
 button:hover, button:focus {
	 border-color: var(--hover);
	 color: #fff;
}
 body {
	 color: #fff;
	 background: #17181c;
	 font: 300 1em 'Fira Sans', sans-serif;
	 justify-content: center;
	 align-content: center;
	 align-items: center;
	 text-align: center;
	 min-height: 100vh;
	 display: flex;
}
 button {
	 background: none;
	 border: 2px solid;
	 font: inherit;
	 line-height: 1;
	 margin: 0.5em;
	 padding: 1em 2em;
}
 h1 {
	 font-weight: 400;
}
 code {
	 color: #e4cb58;
	 font: inherit;
}
 

Live demo

Hope it will be helpful for you.