Should an "unsaved changes" dialog in a web app contain a "save" option?

When a user makes some changes in a web app and tries to navigate away without saving them, a dialog appears as a confirmation/warning message.

There are two approaches to these dialogues. Sometimes they contain the options "Discard, Save, Cancel", and sometimes there's no Save option, and the buttons are just "Discard, Cancel" (whatever the exact phrasing may be, that's not the point).

With Save option (on desktop)

enter image description here

Without Save option enter image description here

The way I see it, the main advantage of the first approach is to not force the user to backtrack - it's reasonable that she might want to save the changes she'd made, so why not help her.

The main advantage of the second approach is probably to make sure that the user sees the changes she's committing. Also, to some extent it helps the user to learn to use the system properly (saving her work manually). Also, a dialog with two options is easier to process than one with three options.

Should this kind of dialog contain a Save option or not?

The setting is an enterprise app for IT management, so the changes impact a lot of things in the organization, it's not something for personal use.

(There are many related questions on the site but I couldn't find one dealing with this specific question).

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