<div class="swiper-container">
  <div class="swiper-wrapper">
    <div class="swiper-slide">
      <!-- アニメーションのクラス名（posChg1 など）が変わっているのみ -->
      <div class="slide-img posChg1" style="background-image: url('images/swiper_img_01.jpg')"></div>
      <div class="slide-content">
        <h1 class="from_top">Slide Title 01</h1>
        <p>Lorem ipsum dolor sit amet, consectetur</p>
        <div class="caption">caption 01</div>
      </div>
    </div>
    <div class="swiper-slide">
      <div class="slide-img posChg2" style="background-image: url('images/swiper_img_02.jpg')"></div>
      <div class="slide-content">
        <h2 class="from_left">Slide Title 02</h2>
        <p class="from_right">Ipsa, quis ex repudiandae eum </p>
        <div class="caption">caption 02</div>
      </div>
    </div>
    <div class="swiper-slide">
      <div class="slide-img posChg3" style="background-image: url('images/swiper_img_03.jpg')"></div>
      <div class="slide-content">
        <h3 class="from_bottom">Slide Title 03</h3>
        <p>Ullam rerum quasi libero esse </p>
        <div class="caption">caption 03</div>
      </div>
    </div>
  </div><!-- end of .swiper-wrapper -->
  <div class="swiper-pagination swiper-pagination-white"></div>
  <div class="swiper-button-prev"></div>
  <div class="swiper-button-next"></div>
</div><!-- end of .swiper-container -->

/* 変更及び追加部分 */
.swiper-container{
  max-width: 720px; /* 最大幅を設定（背景画像より小さく設定） */
}
.slide-img {  
  height: 500px;   /* 表示される画像の幅が表示される領域の幅より小さくなるように高さを調整 */
  background-size: cover;
  background-position: center center;
  background-repeat: no-repeat;
  overflow:visible;
}

@keyframes posChg1 {
  0% {
    background-position: 100% center;
    /*background-position: right center; と同じ*/
  }
  100% {
    background-position: center center;
  }
}
.swiper-slide-active .posChg1 {
  animation: posChg1 6s linear 0s 1 normal both;
} 
@keyframes posChg2 {
  0% {
    background-position: 70% center;
  }
  100% {
    background-position: 30% center;
  }
}
.swiper-slide-active .posChg2 {
  animation: posChg2 6s linear 0s 1 normal both;
} 
@keyframes posChg3 {
  0% {
    background-position: center center;
  }
  100% {
    background-position: 100% center;
    /*background-position: right center; と同じ*/
  }
}
.swiper-slide-active .posChg3 {
  animation: posChg3 6s linear 0s 1 normal both;
} 

/* 変更及び追加部分 ここまで */


.swiper-slide .slide-content h1, .swiper-slide .slide-content h2, .swiper-slide .slide-content h3 {
  position: absolute;
  top: 20%;
  left: 50%;
  transform: translate(-50%, -50%);
  color: #FFF;
  font-size: 30px;
  text-shadow: 2px 2px rgba(0,0,0,0.3);
}
.swiper-slide .slide-content p {
  position: absolute;
  top: 50%;
  left: 50%;
  transform: translate(-50%, -50%);
  color: #FFF;
  text-shadow: .5px .5px rgba(0,0,0,0.6);
  margin: 0;
  padding: 0;
  font-size: 18px;
}
.swiper-slide .slide-content .caption {
  position: absolute;
  bottom: 30px;
  right: 30px;
  color: #FFF;
  font-size: 16px;
  background-color: rgba(0,127,127,0.5);
  padding: 3px 8px;
}

/* 文字のアニメーション */

@keyframes fromTop {
  0% {
    top: 0%;
    opacity: 0;
  }
  100% {
    top: 20%;
    opacity: 1;
  }
}  
  
@keyframes fromBottom {
  0% {
    top: 80%;
    opacity: 0;
  }
  100% {
    top: 20%;
    opacity: 1;
  }
}  

@keyframes fromleft {
  0% {
    left: 0%;
    opacity: 0;
  }
  100% {
    left: 50%;
    opacity: 1;
  }
}
  
@keyframes fromRight {
  0% {
    left: 100%;
    opacity: 0;
  }
  100% {
    left: 50%;
    opacity: 1;
  }
}
 
/* .from_top を指定した要素のアニメーション */
.swiper-slide-active .from_top {
  animation: fromTop .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_bottom を指定した要素のアニメーション */
.swiper-slide-active .from_bottom {
  animation: fromBottom .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_left を指定した要素のアニメーション */
.swiper-slide-active .from_left {
  animation: fromleft .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_right を指定した要素のアニメーション */
.swiper-slide-active .from_right{
  animation: fromRight .6s ease-in-out .5s 1 normal both;
}

<script>
  let mySwiper = new Swiper ('.swiper-container', {
    loop: true,
    
    pagination: {
      el: '.swiper-pagination',
      clickable: true,
    },

    navigation: {
      nextEl: '.swiper-button-next',
      prevEl: '.swiper-button-prev',
    },

  })
</script>