Subscriptions: use new plugin template registration API for subscription templates

In Jetpack Newsletters, we use a bit complicated way (as there wasn't an API before) to register templates that people can use to modify subscription popups, overlays and such. Basically each of these "preview and edit" links opens a pre-defined template:


There's now a new official API we can migrate to:
- https://github.com/WordPress/gutenberg/pull/61577

This will ensure better compatibility and stability of the functionality going forward, as well better example within the codebase for others at a8c and the community how to do something like this.

We'll need to make sure that previously saved modifications are carried over to new system.

Start by locating the Jetpack Newsletters code that registers the subscription popup and overlay templates, then compare its approach with Gutenberg PR 61577. Migrate the registration to the new API and verify that previously saved template modifications remain available in the new system.

Written by the indexing model from the issue text.