Media: Unify remote file upload handler registration logic

[tyxla]

As suggested by @mdawaffe, in #13256 (comment) the logic we introduced in #13253 for splitting the remote media upload handler registration and the jetpack auth didn't make much sense. This follows his advice to unify the handler registration logic, and make it clear that the Jetpack auth is needed specifically by the remote file upload requests.

Changes proposed in this Pull Request:

• Media: Unify remote file upload handler registration logic

Is this a new feature or does it add/remove features to an existing part of Jetpack?

• Alternative to Media: Remove unnecessary XMLRPC/XHR checks from handlers #13256.

Testing instructions:

• Checkout this branch on a connected Jetpack site.
• Try uploading a file via Calypso and make sure it works correctly.

Proposed changelog entry for your changes:

• Media: Unify remote file upload handler registration logic

[jetpackbot]

Thank you for the great PR description!

When this PR is ready for review, please apply the [Status] Needs Review label. If you are an a11n, please have someone from your team review the code if possible. The Jetpack team will also review this PR and merge it to be included in the next Jetpack release.

Scheduled Jetpack release: September 3, 2019.
Scheduled code freeze: August 27, 2019

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[mdawaffe]

LGTM ;) Thanks!

I could see the file upload feature being its own package some day, but there's no need for it now.