iOS search button doesn't work while suggesting input values with LiveView

Hello!
As the title says - I’ve got a problem with iOS search button on the iPhone. I want the iOS search button redirect to the search page with given parameter. If the suggestions in the Live View module are available and suggested input is chosen while clicking on the search button - nothing happens (if the suggestion is not chosen the flow is the same). Once the suggestions are off the button works fine and redirects me to search with given parameter.

<%= form_for :search, Routes.search_path(@socket, :index), [phx_change: "suggest", method: :get], fn f -> %>
  <input type="search" name="search" list="matches" autocomplete="off"  />
  <button type="submit"></button>
  <datalist id="matches">
    <%= for match <- @matches do %>
      <option value="<%= match %>"><%= match %></option>
    <% end %>
  </datalist>
<% end %>

defmodule MyAppWeb.IndexSearchLive do
  # uses
  use Phoenix.LiveView

  # aliases
  alias MyAppWeb.PageView

  # imports
  import MyAppWeb.LiveSuggestionsHelper

  def mount(_params, %{"locale" => locale}, socket) do
    Gettext.put_locale(locale)

    socket = assign(socket, matches: [])
    {:ok, socket}
  end

  def handle_event("suggest", %{"search" => location}, socket)
      when location not in ["", nil] do
    if String.length(location) >= 1 do
      {:noreply, assign(socket, matches: suggest(location))}
    else
      {:noreply, assign(socket, matches: [])}
    end
  end # - once this function is commented the search button works fine, but there are no suggestions

  def handle_event(_event, _params, socket) do
    {:noreply, assign(socket, unhandled: true)}
  end

  def render(assigns) do
    PageView.render("search.html", assigns)
  end
end

I think that type="search and name="search" is obligatory for the iOS search button to work - however if I am wrong please correct me.

I would really appreciate any kind of advice.

Edit: When I say iOS search button I mean the system one, which appears in the system keyboard while typing, the blue one in the right bottom corner