Paint selected row vue js

Below I show what I want to achieve. I have a button in a simple-table. That its function is to select the row in which I am standing. Look for some information, but the only thing I get is that I select the entire row. This is my table.

<v-simple-table fixed-header height="300px">
    <template v-slot:default>
      <thead>
        <tr>
          <th class="text-left">Tipo</th>
          <th class="text-left">Numero trabajo</th>
          <th class="text-left">Cliente</th>
          <th class="text-left">Entrega</th>
          <th class="text-left">Comentario</th>
          <th class="text-left">Tareas</th>
          <th class="text-right">Acciones</th>
        </tr>
      </thead>
      <tbody>
        <tr v-for="item in presupuestos" :key="item.id" :style="TheStyle">
          <td>{{ item.tipoPresupuestoString }}</td>
          <td>{{ item.numero }}</td>
          <td>{{ item.cliente.nombre }}</td>
          <td>{{ formatDate(item.fechaEntrega) }}</td>
          <td>{{ item.presupuestoComentarioString }}</td>
          <td>{{ item.tareas }}</td>
          <td class="text-right">
            <v-icon
              title="Seleccionar OT"
              @click="selectedPresupuesto(item)"
              >mdi-tab-search</v-icon
            >
            <v-icon title="Nueva Tarea" @click="abrirPopupNuevaTarea(item)"
              >mdi-hospital</v-icon
            >
            <v-icon
              title="Listado de Tareas"
              @click="abrirPopupListadoTarea(item)"
            >
              mdi-archive-edit-outline
            </v-icon>
            <v-icon
              title="Agregar comentario"
              class="ml-2"
              @click="popUpComentario(item)"
              >mdi-message</v-icon
            >
            <v-icon title="Descargar" class="text-center" @click="download(item)"
              >mdi-download</v-icon
            >
          </td>
        </tr>
      </tbody>
    </template>
  </v-simple-table>

Through this icon that has the @click="selectedBudget(item)", I have to select the entire row. (in the item comes all the data)

    data() {
return {
  selected: false,
  TheStyle: {
    backgroundColor: "",
  },
};

And here the method:

selectedPresupuesto(item) {
  this.presupuestoSeleccionado = item;
  this.$data.TheStyle.backgroundColor = "grey";
},

attached screen image:

enter image description here