Refactor the watcher (and their tests) to make some methods private

[enricobattocchi]

Context

Summary

This PR can be summarized in the following changelog entry:

• Refactor the watchers (and their tests) to make some methods private.

Relevant technical choices:

Test instructions

Test instructions for the acceptance test before the PR gets merged

This PR can be acceptance tested by following these steps:

Relevant test scenarios

• Changes should be tested with the browser console open
• Changes should be tested on different posts/pages/taxonomies/custom post types/custom taxonomies
• Changes should be tested on different editors (Default Block/Gutenberg/Classic/Elementor/other)
• Changes should be tested on different browsers
• Changes should be tested on multisite

Test instructions for QA when the code is in the RC

• QA should use the same steps as above.

QA can test this PR by following these steps:

Impact check

This PR affects the following parts of the plugin, which may require extra testing:

UI changes

• This PR changes the UI in the plugin. I have added the 'UI change' label to this PR.

Documentation

• I have written documentation for this change. For example, comments in the Relevant technical choices, comments in the code, documentation on Confluence / shared Google Drive / Yoast developer portal, or other.

Quality assurance

• I have tested this code to the best of my abilities
• I have added unittests to verify the code works as intended

Innovation

• No innovation project is applicable for this PR.
• This PR falls under an innovation project. I have attached the innovation label and noted the work hours.

Fixes #

[coveralls]

Pull Request Test Coverage Report for Build 10949487812

Details

• 35 of 36 (97.22%) changed or added relevant lines in 3 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage remained the same at 50.122%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
src/watchers/original-post-watcher.php	6	7	85.71%

Totals
Change from base Build 10041983180:	0.0%
Covered Lines:	1236
Relevant Lines:	2466

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💛 - Coveralls