Add filter for post statuses in quickedit - Refreshing 36237.patch

[SirLouen]

Refreshing and Improving 36237.patch
I've code reviewed it and compared to the original version, there was a little difference on the conditionals (adding Private status type too early).
I am not sure if this was implemented by the original author on purpose @kakomap because there doesn't seem to be an explanation on this.

Apart from this, everything looks good, a nice DRY refactor, meant to include the filter accordingly.

I will be posting a test to this refresh
Automated could be done through Playwright. But I would leave this for further iterations. If anyone wants to add this feel free.
Trac ticket: https://core.trac.wordpress.org/ticket/36237

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Props sirlouen, mukesh27.

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