Syntax for using component with stock Rails 7 application.js setup

[dvodvo]

The stimulus component affirms that the controller should read as follows

import { Application } from '@hotwired/stimulus'
import PasswordVisibility from 'stimulus-password-visibility'

const application = Application.start()
application.register('password-visibility', PasswordVisibility)

when most controllers are initialized as import { Controller } from "@hotwired/stimulus"

The naming of the controller is apparently agnostic to its contents, as the documentation suggests index.js. The following case uses passwordview_controller.js

Whatever the attempts, in the following three variants, the following errors are encountered in the browser console:
import { Application } / Application.start()

import { Controller } / Application.start()

import { Controller } / Controller.start()

config/importmap.rb includes pin "stimulus-password-visibility", to: "https://ga.jspm.io/npm:stimulus-password-visibility@2.0.0/dist/stimulus-password-visibility.es.js"

view set to

<div data-controller="password-visibility">
    <input type="password" data-password-visibility-target="input" spellcheck="false" style='appearance: none; display: block; margin: 0; padding: 8px 12px 8px 48px; tab-size: 4;' />
    <button type="button" data-action="password-visibility#toggle" style='cursor: pointer; display: flex; margin: 0; padding: 0 12px 0 0; position: absolute; right: 0px; text-transform: none; top: 0px;' >
      <span data-password-visibility-target="icon"><%= fa_icon('eye', class: 'fa-1g') %></span>
      <span data-password-visibility-target="icon" class="hidden"><%= fa_icon('eye-slash', class: 'fa-1g') %></span>
    </button>
</div>

do note that there is a css issue, where buttons appear below the input field, which was subject to a failed attempted to be fixed here, in an initial case, before defining a specific class for this use-case, via style definitions (tailwind is uber-view-polluting IMHO) - may require a different issue

GIven the rails out-of-the-box contents of javascript/application.js

import { Application } from "@hotwired/stimulus"

const application = Application.start()

// Configure Stimulus development experience
application.debug = false
window.Stimulus   = application

export { application }

how should this component be effectively written?

This is pertinent to all these components as they follow an identical pattern...

[dvodvo]

Also note that replacing the controller with the contents of the source code leads to this error: