Remove "private" assignation from _deprecated_...() and _doing_it_wrong()

[jrf]

​`_deprecated_function()` was introduced in WP 2.5.0 via [6514] in response to #4361
​`_deprecated_file()` was introduced in WP 2.5.0 via [6514] in response to #4361
​`_deprecated_argument()` was introduced in WP 3.0.0 via [12536] in response to #11386
​`_doing_it_wrong()` was introduced in WP 3.1.0 via [16939] in response to #15824
​`_deprecated_constructor()` was introduced in WP 4.3.0 via [32989] in response to #31982

All of these functions are currently marked as private.

I have not been able to discover why they were marked as private in the first place, but not withstanding that, they are widely used by ​plugins (13249 matches) and ​themes (13512 matches) anyway.

In contrast, ​`do_action_deprecated()` and ​`apply_filters_deprecated()` are not marked private.

Aside from this being inconsistent, IMO, it also doesn't make sense.

Why would plugins and themes not be allowed to use these functions to throw appropriate error notices when (add-on) plugins and (child) themes would be using functionality which the plugin/theme has deprecated ?

So, with this ticket I'd like to propose removing the private assignation from the above mentioned functions.

N.B.: I'm explicitly excluding ​`_deprecated_hook()` from this ticket as that function really shouldn't be called directly, but is invoked under the hood by the do_action_deprecated() and apply_filters_deprecated() functions.

[jrf]

Remove private assignation from _deprecated_..() and _doing_it_wrong() functions

[SergeyBiryukov]

In 46602:

Docs: Remove "private" designation from _doing_it_wrong() and related functions:

• _deprecated_function()
• _deprecated_argument()
• _deprecated_constructor()
• _deprecated_file()

Plugins and themes should be allowed to use these functions to throw appropriate error notices.

This brings them in line with newer do_action_deprecated() and apply_filters_deprecated() functions, which are not marked as private.

Props jrf.
Fixes #48251.