<button @click="buttonClick(1)" :class="buttonIndex == 1?'bgcolor':''">月</button>
<button @click="buttonClick(2)" :class="buttonIndex == 2?'bgcolor':''">季</button>
<button @click="buttonClick(3)" :class="buttonIndex == 3?'bgcolor':''">年</button>

data(){
    buttonIndex:1,
}
 methods:{
    buttonClick(buttonIndex){
          this.buttonIndex = buttonIndex
      }, 
}

.bgcolor {
     background-color: #0066FF;
     border: 0;
     outline: none;
 }
button {
    padding:0.2rem 1.2rem ;
     background: #4E6FFF;
    border: 0;
    color: white;
    border-radius:0 ;
}
button:focus{outline:0;}