Configuration 

This extension ships its frontend TypoScript and its backend page TSconfig in two forms: as TYPO3 site sets, and as classic static templates plus page TSconfig files that are selected on a page. Both forms read the very same files, so they configure an installation identically.

Pick one of them per site and stay with it — see Do not combine both for what happens otherwise.

What the sets contain 

The extension ships the ProfileEditing component and one aggregate set that keeps the stable extension-level set name.

Set Delivers
fgtclb/academic-persons-edit-profile-editing The assigned-profile list, profile editor, AJAX page type and the page TSconfig that offers ProfileEditing in the backend.
fgtclb/academic-persons-edit ProfileEditing under the stable aggregate name. This is the normal set to use.

Both depend on fgtclb/academic-base-ctype-group, the set of EXT:academic_base that labels the content element group all academic extensions sort their elements into.

The plugin renders partials of EXT:academic_persons, but it reads them from Resources/, not from that extension's TypoScript. There is therefore no set dependency on any fgtclb/academic-persons-… set, and none is needed.

The content element is hidden by default 

EXT:academic_persons_edit hides the editing content type for the whole installation and brings ProfileEditing back per component. Whichever of the two mechanisms below you use, ProfileEditing is the only profile-editing content element offered in the backend.

Include the site set 

Add the set to the config.yaml of the site that should offer the content element:

config/sites/my-site/config.yaml (diff)
 base: 'https://example.com/'
 rootPageId: 1
+dependencies:
+  - fgtclb/academic-persons-edit
Copied!

See also TYPO3 Explained, Using a site set as dependency in a site.

The View action in the assigned-profile list uses the same public detail page as the Academic Persons list plugins. Configure plugin.tx_academicpersons.detailPid in the Academic Persons site settings or TypoScript constants. ProfileEditing copies that value into its own Extbase settings and targets the academicpersons_detail content element; it does not require a second page setting in Academic Persons Edit.

Include static templates 

For an installation that still configures its frontend through sys_template records, the same files are registered as static templates and as selectable page TSconfig files.

Include static TypoScript 

Edit the sys_template record of the site root and add the entry to Include static (from extensions):

Entry Delivers
Academic Persons Edit: Profile editing (academic_persons_edit) The TypoScript and AJAX page type of ProfileEditing.
Academic Persons Edit: All components (academic_persons_edit) Every component this extension ships, in one entry.

Include static page TSconfig 

Edit the page record of the site root, tab Resources, field Page TSconfig, and add the entry:

Entry Delivers
Academic Persons Edit: Profile editing (academic_persons_edit) Makes ProfileEditing selectable and configures its wizard entry.
Academic Persons Edit: All components (academic_persons_edit) Every component this extension ships, in one entry.

The setting is inherited by every page below the one it is set on.

Do not combine both 

A site that uses the site set and the static template reads the shipped files twice. The site set is applied before the sys_template record, so the second read happens after the site settings and after config/sites/<site>/constants.typoscript — and it resets every constant the extension ships a default for back to that default.

Nothing else is damaged: the Constants and Setup fields of the sys_template record, the page TSconfig of a page and the page TSconfig files selected on a page are all applied afterwards and still win. Use one mechanism per site and the question does not arise.