Please do pull in work or start something on the final day of the Sprint if you want to.
Don't let anyone tell you you're not allowed to do that. Carry-overs? Who the hell cares?
Don't let the Sprint be a straitjacket that prevents adaptability or doing what's right in the moment.
The Sprint is supposed to be flexible, and if you've met the Sprint Goal, there's no reason not to work on the things that truly matter because someone makes up some kind of artificial Sprint boundary.
I repeat: the goal is never to complete all the work you add at the beginning of the Sprint.
In fact, don't even add all your work at the beginning of the Sprint. That's an anti-pattern because your estimates will be off. Pushing in work means you'll likely bite off more than you can chew. Pull in work gradually, and let the reality of the work dictate how much work you can pull in.
Simply begin with a Sprint Goal, and let every step you take help shape the way.
The more we try to prevent sucking at predicting, the more we will guarantee to suck at adapting.
Keep your boots on the ground and begin with humble plans.