This looks unrelated to the PHP-API-for-Wikisource PHP package at https://github.com/wikisource/api , hence removing that tag.
Assuming this is about ProofreadPage.

In general: It would be welcome to structure tasks by providing 1) steps to reproduce the problem via links, 2) expected outcome, and 3) actual outcome. See https://mediawiki.org/wiki/How_to_report_a_bug for more information. You can edit the task description by clicking Edit Task.

which would toggle open or close both the header and footer in the Wikisource page namespace?

"Header and footer" refers to being in "Edit" mode, I assume?

this feature is available on the enhanced editing toolbar with the use of a mouse

How? Steps to reproduce welcome/needed. On https://en.wikisource.org/wiki/Special:Preferences#mw-prefsection-editing I have "Enable enhanced editing toolbar" enabled but on https://en.wikisource.org/w/index.php?title=Page:Arthur_Stranger--The_Stranger.djvu/14&action=edit but I have no idea how to hide Header and Footer sections with my mouse?

My apologies,

This image https://en.wikisource.org/wiki/File:Header-footer_toggle.jpg shows a page in edit mode! and the toolbar button which uses the [+] as the icon image. For this to be seen, the enhanced editing toolbar has to be enabled on User Preferences\edit tab. The Proofread tools sub menu of the enhanced toolbar must be selected for the controls to appear. Both the header and footer access (open and close) is controlled by the same button.

Thanks. https://en.wikisource.org/w/index.php?title=Page:Arthur_Stranger--The_Stranger.djvu/14&action=edit&debug=true&uselang=qqx shows that this button is proofreadpage-button-toggle-visibility-label in the tooltip

Thanks again for following it up. Now the question remains if it is doable within the Alt-Shift key assignments scheme. The timetable of implementation is less important.