Fix Email Subscriptions saving state

[CGastrell]

Part of DOTCOM-13037

Proposed Changes

This PR replaces the submit button with WP component/button and addresses the design issues with the button saving states.

Why are these changes being made?

Because of design review DOTCOM-12890

Testing Instructions

Go to wordpress.com/me and navigate to the Email Subscriptions tab. See the button is now styled as the buttons on other tabs (or refer to DOTCOM-13037 thread for design references).

Screen.Recording.2025-05-09.at.13.49.13.mov

Pre-merge Checklist

• Has the general commit checklist been followed? (PCYsg-hS-p2)
• Have you written new tests for your changes?
• Have you tested the feature in Simple (P9HQHe-k8-p2), Atomic (P9HQHe-jW-p2), and self-hosted Jetpack sites (PCYsg-g6b-p2)?
• Have you checked for TypeScript, React or other console errors?
• Have you used memoizing on expensive computations? More info in Memoizing with create-selector and Using memoizing selectors and Our Approach to Data
• Have we added the "[Status] String Freeze" label as soon as any new strings were ready for translation (p4TIVU-5Jq-p2)?
  • For UI changes, have we tested the change in various languages (for example, ES, PT, FR, or DE)? The length of text and words vary significantly between languages.
• For changes affecting Jetpack: Have we added the "[Status] Needs Privacy Updates" label if this pull request changes what data or activity we track or use (p4TIVU-aUh-p2)?

[github-actions]

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[matticbot]

Here is how your PR affects size of JS and CSS bundles shipped to the user's browser:

Sections (~22 bytes added 📈 [gzipped])

name                   parsed_size           gzip_size
notification-settings        +81 B  (+0.0%)      +22 B  (+0.0%)

Sections contain code specific for a given set of routes. Is downloaded and parsed only when a particular route is navigated to.

Legend

What is parsed and gzip size?

Parsed Size: Uncompressed size of the JS and CSS files. This much code needs to be parsed and stored in memory.
Gzip Size: Compressed size of the JS and CSS files. This much data needs to be downloaded over network.

Generated by performance advisor bot at iscalypsofastyet.com.