REST API: Revert naming to RequestProcessor and RequestAuthenticator

[itsmeichigo]

Closes: #8453

Description

When working on #8569, I renamed RequestProcessor and RequestAuthenticator to have the ApplicationPassword to be more specific and avoid confusion with CookieNonceAuthenticator.

@selanthiraiyan clarified that these handle not only application password but also WPCom token. So this PR aims to revert that naming.

Testing instructions

Login with site credentials and application password should still work as before.

• Enable the feature flag applicationPasswordAuthenticationForSiteCredentialLogin and build the app.
• Log out of the app or skip onboarding if needed.
• On the prologue screen, select Enter your site address and proceed with the address of your test site.
• Log in with your site credentials. Notice that the login succeeds.

Screenshots

N/A

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• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

[wpmobilebot]

You can test the changes from this Pull Request by:

• Clicking here or scanning the QR code below to access App Center
• Then installing the build number pr8693-6ce8602 on your iPhone

If you need access to App Center, please ask a maintainer to add you.

[selanthiraiyan]

🚢