Place the floating label inside another input-group div.

<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/all.min.css" rel="stylesheet"/>
<script src="https://cdn.jsdelivr.net/npm/bootstrap@5.1.0/dist/js/bootstrap.bundle.min.js"></script>
<link href="https://cdn.jsdelivr.net/npm/bootstrap@5.1.0/dist/css/bootstrap.min.css" rel="stylesheet"/>

<div class="input-group mb-3">
  <div class="form-floating flex-grow-1">
      <input type="text" class="form-control" name="code1" placeholder="Code 1">
      <label for="code1">Code 1</label>
  </div>
  <span class="input-group-text"><i class="fas fa-times"></i></span>
</div>

To improve the answer by @Unmitigated I ended up removing the radius for both right-hand corners of the input.

.form-floating-group input {
  border-bottom-right-radius: 0;
  border-top-right-radius: 0;
}

<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/all.min.css" rel="stylesheet"/>
<script src="https://cdn.jsdelivr.net/npm/bootstrap@5.1.0/dist/js/bootstrap.bundle.min.js"></script>
<link href="https://cdn.jsdelivr.net/npm/bootstrap@5.1.0/dist/css/bootstrap.min.css" rel="stylesheet"/>

<div class="input-group mb-3">
  <div class="form-floating form-floating-group flex-grow-1">
      <input type="text" class="form-control" name="code1" placeholder="Code 1">
      <label for="code1">Code 1</label>
  </div>
  <span class="input-group-text"><i class="fas fa-times"></i></span>
</div>

.input-group .form-floating input {
    border-top-right-radius: 0!important;
    border-bottom-right-radius: 0!important;
}

thanks for the proper nesting, why use a new class namespace?

I encountered the same needs.

Here's my solution:

The form :

<div class="col-12">
  <div class="input-group mb-3">
    <span class="input-group-text">Label :</span>
    <div class="form-floating">
      @Html.EditorFor(model => model.FieldA, new { htmlAttributes = new { @class = "form-control", placeholder = "Field A" } })
      @Html.LabelFor(model => model.FieldA)
    </div>
    <div class="form-floating">
      @Html.EditorFor(model => model.FieldB, new { htmlAttributes = new { @class = "form-control", placeholder = "Field B" } })
      @Html.LabelFor(model => model.FieldB)
    </div>
  </div>
</div>

Note : i'm using ASP.NET, replace Editor and Label -For calls with your corresponding code :

<input type="text" class="form-control" name="code1" placeholder="Code 1">
<label for="code1">Code 1</label>
<span class="input-group-text"><i class="fas fa-times"></i></span>

Find Bootstrap original way (V5.1) of handling rounded border. Here are the original code lines :

.input-group:not(.has-validation) > :not(:last-child):not(.dropdown-toggle):not(.dropdown-menu),
.input-group:not(.has-validation) > .dropdown-toggle:nth-last-child(n+3) {
  border-top-right-radius: 0;
  border-bottom-right-radius: 0;
}
.input-group.has-validation > :nth-last-child(n+3):not(.dropdown-toggle):not(.dropdown-menu),
.input-group.has-validation > .dropdown-toggle:nth-last-child(n+4) {
  border-top-right-radius: 0;
  border-bottom-right-radius: 0;
}
.input-group > :not(:first-child):not(.dropdown-menu):not(.valid-tooltip):not(.valid-feedback):not(.invalid-tooltip):not(.invalid-feedback) {
  margin-left: -1px;
  border-top-left-radius: 0;
  border-bottom-left-radius: 0;
}

.input-group > .form-control,
.input-group > .form-select {
  position: relative;
  flex: 1 1 auto;
  width: 1%;
  min-width: 0;
}

And here's my custom css based on what I know of css selectors (I'm actually a backend dev) :

.input-group:not(.has-validation) .form-floating:not(:last-child) > :not(.dropdown-toggle):not(.dropdown-menu),
.input-group:not(.has-validation) .form-floating > .dropdown-toggle:nth-last-child(n+3) {
  border-top-right-radius: 0;
  border-bottom-right-radius: 0;
}
.input-group.has-validation .form-floating:nth-last-child(n+3) > :not(.dropdown-toggle):not(.dropdown-menu),
.input-group.has-validation .form-floating > .dropdown-toggle:nth-last-child(n+4) {
  border-top-right-radius: 0;
  border-bottom-right-radius: 0;
}
.input-group .form-floating:not(:first-child) > :not(.dropdown-menu):not(.valid-tooltip):not(.valid-feedback):not(.invalid-tooltip):not(.invalid-feedback) {
  /*margin-left: -1px;*/
  border-top-left-radius: 0;
  border-bottom-left-radius: 0;
}

/* for form to be responsive */
.input-group > .form-floating {
  position: relative;
  flex: 1 1 auto;
  width: 1%;
  min-width: 0;
}

I guess the selectors could be greatly improved, as some cases could no more occur, feel free to submit improvements !

Classes rounded-0 rounded-start needed to avoid border-radius at the right of input text

<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/all.min.css" rel="stylesheet" />
<script src="https://cdn.jsdelivr.net/npm/bootstrap@5.1.0/dist/js/bootstrap.bundle.min.js"></script>
<link href="https://cdn.jsdelivr.net/npm/bootstrap@5.1.0/dist/css/bootstrap.min.css" rel="stylesheet" />

<div class="container mt-5">
  <div class="input-group">
    <div class="flex-grow-1 form-floating">
      <input placeholder="Search address" aria-label="Search address" aria-describedby="basic-wallet" type="text" class="rounded-0 rounded-start form-control" value="New York">
      <label>Your wallet address</label>
    </div>
    <span class="input-group-text"><i class="fas fa-times"></i></span>
  </div>
</div>