The "Next tag badge" and "Newest" badge widget have this button:
But "Next badge" widget doesn't:
Can you add the button on this popup to open the badge page?
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Those are two different buttons; if you've earned the badge (your 'Popular Question' screenshot), the popup will always show a "Learn more >" button which will take you to your personal badge page where you can see how often you've earned that particular badge.
The popup related to the progress will show a "Go get it >" button if there's a meaningful page to show you. For example, when tracking the Socratic badge, it will take you to the Ask a Question page:
Other badges might take you to other pages. However, TPTB have decided that there's no good target page for the Marshal badge. Now that I think of it, the First Posts review queue might be a viable option; on some sites, I cast quite a few Not An Answer flags and close flags for them. There's a precedent for linking to review queues; if you have enough reputation to edit posts, the "Go get it" button for the Copy Editor badge takes you to the Low Quality Posts review queue.