Convert the messages to shoelace toast?

Problem/Motivation

We are currently displaying some error messages in a area of the display builder:

  <div class="display-builder__main">
    <span id="message-{{ builder_id }}"></span>
    {{ view_main }}
  </div>

See RenderableBuilderTrait::buildError().

And we want to also use this area for notifications: [3542797]

However, it seems shoelace alerts is not the best component for this kind of messages because of the duration management.

Proposed resolution

Use shoelace's toast instead of alerts?