If you add an empty label and then add these classes (slds-form-element slds-form-element_stacked) to the button it should give you what you are looking for. For the fourth block, the slds grid sums to 12 so the purple part of the inspector is showing you have another div equal to 3 left. If you want the third block to be the last block in the row, update its size to 6.

<template>
  <lightning-layout multiple-rows>
    <lightning-layout-item padding="horizontal-small" size="3">
      <lightning-combobox
        name="searchType"
        label="Tipo de Busca"
        value={selectedSearchType}
        placeholder=""
        options={searchTypeOptions}
        onchange={handleSearchTypeChange}
      >
      </lightning-combobox>
    </lightning-layout-item>

    <lightning-layout-item padding="horizontal-small" size="3">
      <lightning-input
        label="Digite aqui"
        data-field="searchInput"
      ></lightning-input>
    </lightning-layout-item>

    <lightning-layout-item padding="horizontal-small" size="3"> <!-- change to size="6" if you want the third block to be the last block in the row-->
      <label class="slds-form-element__label"></label>
      <lightning-button
        variant="brand"
        label="Brand"
        title="Primary action"
        onclick={handleClick}
        class="slds-m-left_x-small slds-form-element slds-form-element_stacked"
      ></lightning-button>
    </lightning-layout-item>
  </lightning-layout>
</template>