I made another variant with dropdown menu (perhaps for advanced search etc).. Here is how it looks like:
<div class="input-group my-4 col-6 mx-auto">
<input class="form-control py-2 border-right-0 border" type="search" placeholder="Type something..." id="example-search-input">
<span class="input-group-append">
<button type="button" class="btn btn-outline-primary dropdown-toggle dropdown-toggle-split border border-left-0 border-right-0 rounded-0" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
<span class="sr-only">Toggle Dropdown</span>
</button>
<button class="btn btn-outline-primary rounded-right" type="button">
<i class="fas fa-search"></i>
</button>
<div class="dropdown-menu dropdown-menu-right">
<a class="dropdown-item" href="#">Action</a>
<a class="dropdown-item" href="#">Another action</a>
<a class="dropdown-item" href="#">Something else here</a>
<div role="separator" class="dropdown-divider"></div>
<a class="dropdown-item" href="#">Separated link</a>
</div>
</span>
</div>
Note: It appears green in the screenshot because my site main theme is green.