Use core's new centralized file upload service for file upload logic

Problem/Motivation

Core has done a ton of work recently to centralize the file upload logic in a service as there was a lot of duplication among various core modules (REST and JSON:API for example). We should take advantage of that to reduce our code footprint.

See 📌 [META] Modernise file upload logic Active

Steps to reproduce

Proposed resolution

I think 10.3.x is the version that includes all of what we need. So, wait until 10.3 is the oldest supported version of Drupal, then refactor our code to use it.

Remaining tasks

User interface changes

API changes

Data model changes