RTE and media picker should route medias the same way in the Delivery API

[kjac]

Prerequisites

• I have added steps to test this contribution in the description below

If there's an existing issue for this PR then this fixes #16416

Description

As described in #16416, the Delivery API outputs different media routes for the media picker and medias in RTE. This PR ensures that:

1. Media picker and RTE uses the same implementation (IApiMediaUrlProvider) to calculate media routes in the Delivery API.
2. The Delivery API respects WebRoutingSettings.UrlProviderMode.

Testing this PR

Given a document with a media picker and an RTE (with a media inside), verify that the Delivery API output:

1. Contains the same media route (URL) for both properties.
2. Respects WebRoutingSettings.UrlProviderMode - e.g. setting it to explicitly render absolute URLs.
3. Also works when outputting RTE as JSON.

Breaking change

This PR is behaviourally breaking. But the current behaviour is a bug - it should not behave like that.