Hey, beginner's question here
I'm planinning on adding restriction of the articles to particular user groups and I'd like to add the checkboxes for groups selection from the Edit page
I'm lost though how exactly to add or modify the functionality of Edit form
Have you considered using the already builtin page protection
Modifying edit page isn't the easiest. You can use hooks like manual:hooks/EditPage::importFormData (there are a bunch, that is probably not the best one) to modify public instance variables of the EditPage class, like editFormTextBottom (https://github.com/wikimedia/mediawiki/blob/master/includes/EditPage.php#L353 )
Maybe look at what other extensions do. I think FlaggedRevisions modifies the edit form, so does extension:TemplateSandbox
